Corresponding Angle Relationships (A) - Free Printable

To find the corresponding angle measurements, we need to understand the relationship between angles formed when a transversal line intersects two parallel lines.

Key Rules:
1. Corresponding Angles are Equal: If you look at the same position at each intersection (for example, top-right corner), those angles are equal.
2. Vertical Angles are Equal: Angles opposite each other where lines cross are equal.
3. Supplementary Angles add up to 180°: Angles on a straight line next to each other add up to 180°.

Let's solve each diagram step-by-step.

Diagram 1 (Top Left)

* Given: Top intersection has $134^\circ$ (top-left) and $46^\circ$ (top-right). Bottom intersection has $46^\circ$ (bottom-left).
* Goal: Find the missing angle at the bottom right (inside the parallel lines, on the right side of the transversal). Let's call the angle above it $x$ (top-right position at bottom intersection) and the angle requested is likely the one corresponding to the top-right $46^\circ$.
* Looking at the positions:
* The angle at the top-right of the top intersection is $46^\circ$.
* The corresponding angle at the top-right of the bottom intersection must also be $46^\circ$.
* The angle vertically opposite to that (bottom-left) is given as $46^\circ$, which matches.
* The angle adjacent to it on the straight line CD would be $180^\circ - 46^\circ = 134^\circ$. This corresponds to the top-left angle of $134^\circ$.
* The diagram asks for the measurement corresponding to the measured angles. The blank circle is at the top-right position of the bottom intersection? No, the circle is around the intersection point E. Usually, these worksheets ask you to fill in the specific unmarked angles based on correspondence.
* Let's look at the specific empty spots or implied questions. The prompt says "Find the corresponding angle measurements for the measured angles."
* Angle $134^\circ$ (Top-Left) corresponds to the angle at Bottom-Left? No, Top-Left corresponds to Top-Left.
* Top-Left ($134^\circ$) corresponds to Bottom-Left. The Bottom-Left is marked $46^\circ$? Wait. Let's re-examine Diagram 1.
* Top Intersection: Left is $134^\circ$, Right is $46^\circ$. ($134+46=180$, correct).
* Bottom Intersection: Left is $46^\circ$. This is in the Bottom-Left position.
* The Corresponding Angle to the Top-Right ($46^\circ$) is the Bottom-Right? No. Corresponding angles are in the *same relative position*.
* Top-Right ($46^\circ$) corresponds to Bottom-Right.
* Top-Left ($134^\circ$) corresponds to Bottom-Left.
* In Diagram 1, the bottom-left angle is labeled $46^\circ$. But the top-left is $134^\circ$. These are not equal. This implies the lines might not be parallel or I am misinterpreting the label positions.
* Let's look closer. The arc for $46^\circ$ at the bottom is in the Bottom-Left quadrant. The arc for $134^\circ$ at the top is in the Top-Left quadrant. If lines are parallel, these should be equal. They are not ($134 \neq 46$).
* Ah, looking at the transversal slope: It goes from bottom-left to top-right.
* Top Intersection: Angle $F-A-E$? No, $A$ is left, $B$ is right. $F$ is up.
* Angle between Ray $A$ (left) and Transversal (up) is $134^\circ$? That's an obtuse angle. Visually it looks obtuse.
* Angle between Ray $B$ (right) and Transversal (up) is $46^\circ$. Acute. Correct.
* Bottom Intersection: Ray $C$ (left), Ray $D$ (right). Transversal comes from $E$ (down).
* Angle labeled $46^\circ$ is between Ray $C$ (left) and Transversal (down). This is the Bottom-Left vertical angle? No, it's the angle inside the parallel lines? No, it's below line C. So it is Bottom-Left.
* If Line AB || Line CD, then Top-Left ($134^\circ$) should equal Bottom-Left. But Bottom-Left is labeled $46^\circ$.
* Wait, let's look at Vertical Angles. The angle vertically opposite to the Bottom-Left ($46^\circ$) is the Top-Right (inside the parallel lines).
* Let's re-read the diagram carefully.
* Top: Left=$134$, Right=$46$.
* Bottom: Left=$46$. This angle is vertically opposite to the interior angle on the right? No.
* Actually, usually in these problems, if one angle is given, you find its correspondent.
* Let's assume the question asks to identify the value of the angle that corresponds to the explicitly labeled ones, or simply fill in the blanks. But there are no blanks. The circles are just highlighting the vertex.
* Let's look at Diagram 2. Top has a circle. Bottom has $75, 105, 75$.
* Diagram 3. Top has a circle. Bottom has $31$.
* Diagram 4. Top has $137, 43$. Bottom has $43, 137$. All filled.
* Diagram 5. Top has a circle. Bottom has $142$.
* Diagram 6. Top has $112$. Bottom has $68, 68$.

It seems the task is to find the measure of the angle indicated by the empty circle or simply deduce the missing values based on the "Corresponding Angles" title. However, most diagrams have all numbers filled except for a circle at one intersection. Let's assume the circle indicates the angle(s) we need to determine, or perhaps the diagram is showing examples and we just need to verify/state the relationships.

Actually, looking at the instruction "Find the corresponding angle measurements for the measured angles," it likely means: Identify the angle that corresponds to the given measured angle and state its value. Or, more simply, fill in the missing angle at the circled intersection.

Let's analyze each case assuming we need to find the angles at the circled intersection based on the other intersection.

Diagram 1:
* Top Intersection: Top-Left = $134^\circ$, Top-Right = $46^\circ$.
* Bottom Intersection: Bottom-Left = $46^\circ$.
* Check for consistency: If lines are parallel, Top-Left ($134^\circ$) corresponds to Bottom-Left. Here Bottom-Left is $46^\circ$. This is a contradiction unless the $46^\circ$ label is actually for the Bottom-Right?
* Let's look at the arc. The arc for $46^\circ$ at the bottom is between the transversal (going down-left) and the line C (going left). That is the Bottom-Left angle.
* The arc for $134^\circ$ at the top is between transversal (going up-right) and line A (going left). That is Top-Left.
* These are corresponding angles. They must be equal. $134 \neq 46$.
* Is it possible the $46^\circ$ at the bottom is the vertical angle to the interior angle?
* Let's look at the alternate interpretation: Maybe the $46^\circ$ at the bottom is the angle between the transversal and line D? No, it's clearly on the C side.
* Let's look at the other numbers. Top Right is $46^\circ$. Bottom Left is $46^\circ$. These are Alternate Exterior Angles? No. Top-Right and Bottom-Left are Alternate Exterior Angles. If lines are parallel, Alternate Exterior Angles are equal. $46 = 46$. This works!
* So, the lines ARE parallel.
* The circle is at the bottom intersection. We know Bottom-Left is $46^\circ$.
* We can find the other angles at the bottom intersection:
* Bottom-Right (vertical to Top-Left correspondent? No).
* Bottom-Right is supplementary to Bottom-Left. $180 - 46 = 134^\circ$.
* Top-Right (interior) is vertical to Bottom-Left? No. Vertical to Bottom-Left is Top-Right (interior). So Interior-Right = $46^\circ$? No, Vertical angles are opposite. The angle opposite Bottom-Left is the angle above line D, on the right of the transversal. Let's call it Angle $y$. Angle $y = 46^\circ$.
* The angle corresponding to the Top-Right ($46^\circ$) is the Bottom-Right? No. Top-Right corresponds to Bottom-Right. So Bottom-Right should be $46^\circ$?
* Let's restart the standard positions.
* Pos 1: Top-Left. Pos 2: Top-Right. Pos 3: Bottom-Left. Pos 4: Bottom-Right. (At top intersection)
* Pos 5: Top-Left. Pos 6: Top-Right. Pos 7: Bottom-Left. Pos 8: Bottom-Right. (At bottom intersection)
* Given: Pos 1 = $134$. Pos 2 = $46$.
* Given: Pos 7 = $46$. (Bottom-Left at bottom intersection).
* Correspondence: Pos 1 corresponds to Pos 5. So Pos 5 should be $134$.
* Pos 2 corresponds to Pos 6. So Pos 6 should be $46$.
* Pos 7 (Bottom-Left) is vertical to Pos 6 (Top-Right)? No. Pos 7 is vertical to Pos 6? Let's visualize. Line CD horizontal. Transversal / .
* Pos 5: Above C, Left of Transversal.
* Pos 6: Above D, Right of Transversal.
* Pos 7: Below C, Left of Transversal.
* Pos 8: Below D, Right of Transversal.
* Vertical pairs: (5,8) and (6,7).
* So Pos 7 is vertical to Pos 6.
* We established Pos 6 (corresponding to Top-Right $46$) is $46$.
* Therefore Pos 7 (vertical to Pos 6) is $46$.
* The diagram labels Pos 7 as $46$. This is consistent.
* Conclusion for Diagram 1: The angles at the bottom intersection are:
* Bottom-Left (given): $46^\circ$
* Top-Right (vertical to given): $46^\circ$ (This corresponds to the Top-Right $46^\circ$ at the top).
* Top-Left (supplementary to Top-Right): $180 - 46 = 134^\circ$ (This corresponds to Top-Left $134^\circ$ at the top).
* Bottom-Right (vertical to Top-Left): $134^\circ$.
* The "answer" is likely identifying the corresponding angles. The corresponding angle to the top $134^\circ$ is the bottom-left-top angle ($134^\circ$). The corresponding angle to the top $46^\circ$ is the bottom-right-top angle ($46^\circ$).

Let's simplify. For each diagram, I will provide the measures of the angles at the intersection that has the circle, derived from the other intersection.

Diagram 1 (Top Left):
* Knowns at Top: TL=$134^\circ$, TR=$46^\circ$.
* Circle at Bottom.
* Corresponding angles are equal.
* Angle at Bottom TL (Top-Left position relative to intersection E) corresponds to Top TL. So Bottom TL = $134^\circ$.
* Angle at Bottom TR (Top-Right position) corresponds to Top TR. So Bottom TR = $46^\circ$.
* Angle at Bottom BL (Bottom-Left position) is vertical to Bottom TR. So Bottom BL = $46^\circ$. (Matches given).
* Angle at Bottom BR (Bottom-Right position) is vertical to Bottom TL. So Bottom BR = $134^\circ$.
* Missing values to report: The angles at the circled intersection are $134^\circ$ (Top-Left), $46^\circ$ (Top-Right), $46^\circ$ (Bottom-Left), $134^\circ$ (Bottom-Right).

Diagram 2 (Top Right):
* Knowns at Bottom: TL=$75^\circ$? No, let's look at positions.
* Angle $75^\circ$ is between Line C (left) and Transversal (up). This is Top-Left at the bottom intersection.
* Angle $105^\circ$ is between Line D (right) and Transversal (up). This is Top-Right at the bottom intersection.
* Angle $75^\circ$ is between Line C (left) and Transversal (down). This is Bottom-Left at the bottom intersection.
* Check: $75+105=180$. Correct. Vertical angles $75$ and $75$. Correct.
* Circle at Top.
* We need angles at Top Intersection.
* Corresponding Angles:
* Bottom TL ($75^\circ$) corresponds to Top TL. So Top TL = $75^\circ$.
* Bottom TR ($105^\circ$) corresponds to Top TR. So Top TR = $105^\circ$.
* Bottom BL ($75^\circ$) corresponds to Top BL? No. Bottom-Left corresponds to... wait.
* Standard Correspondence:
* Top-Left corresponds to Top-Left.
* Top-Right corresponds to Top-Right.
* Bottom-Left corresponds to Bottom-Left.
* Bottom-Right corresponds to Bottom-Right.
* So:
* Top TL = Bottom TL = $75^\circ$.
* Top TR = Bottom TR = $105^\circ$.
* Top BL = Bottom BL = $75^\circ$.
* Top BR = Bottom BR. Bottom BR is vertical to Bottom TL ($75^\circ$)? No, vertical to Bottom TL is Top-Right ($105^\circ$)? No.
* Let's stick to simple correspondence.
* Angle at Bottom in "Top-Left" position is $75^\circ$. So Angle at Top in "Top-Left" position is $75^\circ$.
* Angle at Bottom in "Top-Right" position is $105^\circ$. So Angle at Top in "Top-Right" position is $105^\circ$.
* Consequently, the other two angles at the top are $105^\circ$ (Bottom-Left) and $75^\circ$ (Bottom-Right).

Diagram 3 (Middle Left):
* Knowns at Bottom: Angle $31^\circ$ is in the Top-Left position (between Line C and Transversal going up). Wait, the arc is below line C? No, it's above line C, left of transversal. It looks like the acute angle.
* Let's check the slope. Transversal goes bottom-left to top-right.
* Angle $31^\circ$ is marked between Line C (left) and the transversal. It is in the Top-Left quadrant of the bottom intersection.
* Circle at Top.
* Corresponding Angle: The angle in the Top-Left position at the Top Intersection corresponds to the $31^\circ$ angle.
* So, Top TL = $31^\circ$.
* Then, Top TR = $180 - 31 = 149^\circ$.
* Top BL = $149^\circ$ (vertical to TR? No, vertical to TR is BL. Yes).
* Top BR = $31^\circ$ (vertical to TL).

Diagram 4 (Middle Right):
* This diagram has all numbers filled.
* Top: TL=$137$, TR=$43$.
* Bottom: TL=$43$? No. Let's look closely.
* Bottom Left angle is $43^\circ$. Position: Top-Left? No, it's between Line C and Transversal. It's the acute angle. Since the transversal slopes up-right, the Top-Left angle is obtuse?
* Let's check Top: TL=$137$ (Obtuse). TR=$43$ (Acute).
* Bottom: The angle labeled $43^\circ$ is in the Top-Left position? Visually it looks acute. But Top-Left corresponds to Top-Left ($137$). Contradiction?
* Let's look at the position again. The arc for $43^\circ$ is between Line C (left) and the transversal part going DOWN to E. That is the Bottom-Left position.
* The angle labeled $137^\circ$ is between Line D (right) and the transversal part going UP. That is the Top-Right position.
* Let's verify consistency.
* Top TL=$137$. Corresponds to Bottom TL.
* Top TR=$43$. Corresponds to Bottom TR.
* If Bottom TR=$43$, then Bottom TL (supplementary) = $137$.
* The diagram labels an angle $43^\circ$ at the bottom. Where is it? It is in the Top-Left visual quadrant? No, the arc is below line C. So it is Bottom-Left or Bottom-Right? It is to the left of the transversal. So it is Bottom-Left.
* If Bottom-Left is $43^\circ$, then Top-Left (corresponding) should be $43^\circ$. But Top-Left is $137^\circ$.
* There is a mismatch in my position reading or the diagram.
* Let's look at the other bottom angle: $137^\circ$. It is to the right of the transversal, above line C? No, the arc is above line C. So it is Top-Right.
* So Bottom TR = $137^\circ$.
* Top TR = $43^\circ$. Corresponding angles should be equal. $137 \neq 43$.
* Wait, Alternate Interior Angles?
* Top TR ($43$) and Bottom TL (if it were interior) ...
* Let's re-read the arcs carefully.
* Top: Left=$137$, Right=$43$.
* Bottom: Left=$43$, Right=$137$.
* The angle $43^\circ$ at the bottom is in the Top-Left position? No, the arc is clearly below the line C. And to the left of the transversal. So Bottom-Left.
* The angle $137^\circ$ at the bottom is in the Top-Right position? The arc is above line C, right of transversal. So Top-Right.
* If Bottom-Left = $43$ and Bottom-Right (supplementary) = $137$? No, Bottom-Left and Bottom-Right are on a straight line. $43+137=180$. OK.
* But wait, the angle labeled $137$ is above the line. The angle labeled $43$ is below the line.
* Let's assume the labels indicate the value of the angle in that specific corner.
* Bottom-Left (below C, left of trans) = $43^\circ$?
* Top-Right (above C, right of trans) = $137^\circ$?
* These are vertical angles! Vertical angles must be equal. $43 \neq 137$.
* Okay, let's look at the diagram again. Maybe the $43$ is Top-Left (above C, left of trans) and $137$ is Bottom-Right (below D, right of trans)?
* If Bottom TL = $43$, then Top TL (corr) = $43$. But Top TL is $137$.
* If Bottom TR = $137$, then Top TR (corr) = $137$. But Top TR is $43$.
* This implies the lines are NOT parallel? Or I am misidentifying the angles.
* Let's look at Alternate Interior Angles.
* Top Right ($43$) is exterior? No, it's above the parallel line.
* Let's look at Consecutive Interior Angles.
* Maybe the $43$ at the bottom is the Interior Left angle? (Above C, Left of Trans).
* Maybe the $137$ at the bottom is the Interior Right angle? (Above C, Right of Trans).
* If Bottom TL (interior) = $43$ and Bottom TR (interior) = $137$. Sum = $180$.
* Top TL = $137$. Top TR = $43$.
* Correspondence:
* Top TL ($137$) corresponds to Bottom TL. If Bottom TL is $43$, they don't match.
* HOWEVER, if we look at Alternate Interior Angles: Top Right ($43$) and Bottom Left ($43$). These are equal.
* Top Left ($137$) and Bottom Right ($137$). These are equal.
* This confirms the lines are parallel.
* So, for Diagram 4, all angles are already provided. The "task" might just be to recognize them. Since there is no circle, maybe this is an example? Or maybe I need to list the correspondences?
* The prompt says "Find the corresponding angle measurements".
* Corresponding pairs:
* $137^\circ$ (Top Left) corresponds to $137^\circ$ (Bottom Right?? No, Bottom Left??).
* Let's trace: Top-Left ($137$). Corresponding is Bottom-Left.
* In the diagram, the angle in the Bottom-Left position (Above C, Left of Trans) is labeled $43^\circ$?
* Let's look really closely at Diagram 4.
* The angle labeled $43^\circ$ is between Line C and the transversal. The arc is in the upper-left quadrant of the intersection E. So it is Bottom-Top-Left.
* The angle labeled $137^\circ$ is between Line D and the transversal. The arc is in the upper-right quadrant. So it is Bottom-Top-Right.
* So Bottom TL = $43$, Bottom TR = $137$.
* Top TL = $137$, Top TR = $43$.
* Corresponding Angles:
* Top TL ($137$) should equal Bottom TL ($43$). THEY DON'T.
* Top TR ($43$) should equal Bottom TR ($137$). THEY DON'T.
* Are they Alternate Interior?
* Interior angles are between the parallel lines.
* Top Interior Left = $180-137=43$? No, Top TL is exterior? No, "Top-Left" usually means the quadrant.
* Let's assume standard position:
* Line AB is top. Line CD is bottom.
* Angle $137$ is Top-Left (Exterior). Angle $43$ is Top-Right (Exterior).
* Angle $43$ at bottom is Top-Left (Interior). Angle $137$ at bottom is Top-Right (Interior).
* Corresponding Angles are in the same position.
* Top-Left Exterior ($137$) corresponds to Top-Left Interior ($43$). Not equal.
* This suggests the angles labeled are Alternate Interior or similar, NOT corresponding in position value directly unless we rotate?
* Wait. Look at the transversal direction.
* If Top-Left is $137$, then Bottom-Left (Corresponding) MUST be $137$.
* The diagram shows $43$ in that spot.
* Is it possible the $43$ is the Bottom-Left Exterior? (Below C, Left of Trans).
* If Bottom-Left Exterior = $43$, then Vertical Angle (Top-Right Interior) = $43$.
* Top-Right Exterior = $43$.
* Corresponding: Top-Right Exterior ($43$) corresponds to Bottom-Right Exterior.
* This is getting confusing without being able to point.
* Let's trust the math: Parallel lines imply Corresponding Angles are Equal.
* In Diagram 4, we have $137$ and $43$ at top. We have $43$ and $137$ at bottom.
* The angle corresponding to the Top $137^\circ$ (which is in the Top-Left position) is the Bottom-Left position angle. In the diagram, the angle in the Bottom-Left position (visually, above line C, left of transversal) is labeled $43^\circ$. This is a contradiction for "Corresponding Angles are Equal".
* UNLESS: The angle labeled $137$ at the top is Top-Right? No, it's on the left.
* UNLESS: The angle labeled $43$ at the bottom is Bottom-Right? No, it's on the left.
* Let's look at Alternate Exterior Angles. Top-Left ($137$) and Bottom-Right ($137$). Equal.
* Top-Right ($43$) and Bottom-Left ($43$). Equal.
* So the diagram shows that Alternate Exterior/Interior angles are equal.
* But the title is "Corresponding Angles".
* Perhaps the question is just asking to identify the value of the angle that *would* correspond, or maybe the diagram is labeled with Alternate angles and we have to find the Corresponding ones?
* Actually, looking at Diagram 1, 2, 3, 5, 6, they have circles. Diagram 4 does not. Diagram 4 might be a completed example or a "check your understanding" where all answers are present.
* For the purpose of the final answer, I will provide the missing angles for the diagrams with circles.

Diagram 5 (Bottom Left):
* Knowns at Bottom: Angle $142^\circ$ is in the Bottom-Left position (Below C, Left of Trans).
* Circle at Top.
* We need angles at Top.
* Corresponding Angle to Bottom-Left ($142^\circ$) is Top-Left.
* So Top TL = $142^\circ$.
* Then Top TR = $180 - 142 = 38^\circ$.
* Top BL = $38^\circ$ (Vertical to TR? No, Vertical to TR is BL. Wait. Top TR and Top BL are vertical? No. Top TR and Bottom-Left-of-Top-Intersection are vertical. Let's use standard names:
* TL and BR are vertical.
* TR and BL are vertical.
* So if Top TL = $142$, then Top BR = $142$.
* If Top TR = $38$, then Top BL = $38$.

Diagram 6 (Bottom Right):
* Knowns at Bottom:
* Angle $68^\circ$ (Left) is in Bottom-Left position? Arc is below C, left of trans. Yes.
* Angle $68^\circ$ (Right) is in Bottom-Right position? Arc is below D, right of trans. Yes.
* Wait, Bottom-Left and Bottom-Right are supplementary? $68+68=136 \neq 180$.
* Let's re-examine Diagram 6.
* Left angle $68^\circ$: Arc is between Line C (left) and Transversal (down). This is Bottom-Left.
* Right angle $68^\circ$: Arc is between Line D (right) and Transversal (up). This is Top-Right.
* Check Vertical Angles: Bottom-Left and Top-Right are vertical. They should be equal. $68=68$. Consistent.
* Circle at Top.
* We need angles at Top.
* Corresponding Angles:
* Bottom-Left ($68^\circ$) corresponds to Top-Left.
* So Top TL = $68^\circ$.
* Top-Right ($68^\circ$) corresponds to... wait.
* Let's use the Top-Right at bottom ($68^\circ$). It corresponds to Top-Right at top.
* So Top TR = $68^\circ$.
* If Top TL = $68$ and Top TR = $68$, then $68+68=136 \neq 180$.
* Contradiction. Lines cannot be parallel if corresponding angles on a straight line don't sum to 180?
* Top TL and Top TR are supplementary.
* If Top TL corresponds to Bottom-Left ($68$), then Top TL = $68$.
* If Top TR corresponds to Bottom-Right... what is Bottom-Right?
* Bottom-Right is vertical to Bottom-Left? No. Bottom-Right is supplementary to Bottom-Left.
* Bottom-Left = $68$. So Bottom-Right = $180 - 68 = 112^\circ$.
* Top TR corresponds to Bottom-Right. So Top TR = $112^\circ$.
* Check: Top TL ($68$) + Top TR ($112$) = $180$. Correct.
* So, why is there a $68^\circ$ label on the right side of the bottom intersection?
* The label $68^\circ$ on the right is in the Top-Right position (Above D, Right of Trans).
* Top-Right (Bottom Intersection) corresponds to Top-Right (Top Intersection).
* So Top TR should be $68^\circ$.
* But we just calculated Top TR = $112^\circ$.
* Let's re-read the position of the right-side $68^\circ$ in Diagram 6.
* Arc is between Line D and Transversal. It is BELOW Line D? Or ABOVE?
* The transversal goes from bottom-left to top-right.
* The angle is acute.
* The angle between Line D (right) and Transversal (up) is Acute?
* If the transversal is steep, yes.
* If Bottom-Left (obtuse?) No, $68$ is acute.
* If Bottom-Left is $68$ (Acute), then the transversal makes an acute angle with the parallel lines.
* Then Top-Right (Interior) should be alternate interior to Bottom-Left? No.
* Let's assume the label $68^\circ$ on the right is Bottom-Right (Below D, Right of Trans).
* If Bottom-Left = $68$ and Bottom-Right = $68$, they are not supplementary. Impossible for straight line.
* Therefore, one of the $68$s is vertical to the other?
* Left $68$: Below C, Left of Trans (Bottom-Left).
* Right $68$: Above D, Right of Trans (Top-Right).
* These are Vertical Angles. They are equal. This is physically possible.
* So, Bottom-Left = $68$. Bottom-Right (supplementary) = $112$.
* Top-Right (at bottom) = $68$. Top-Left (at bottom) = $112$.
* Now, find Top Intersection angles (Circle).
* Top TL corresponds to Bottom TL ($68$). So Top TL = $68$.
* Top TR corresponds to Bottom TR ($112$). So Top TR = $112$.
* Top BL corresponds to Bottom BL ($112$). So Top BL = $112$.
* Top BR corresponds to Bottom BR ($68$). So Top BR = $68$.
* Note: The diagram also has a label $112^\circ$ at the top?
* Looking at Diagram 6 Top: There is a label $112^\circ$. It is in the Top-Left position?
* Arc is between Line A (left) and Transversal (up). That is Top-Left.
* So Top TL is given as $112^\circ$.
* But we calculated Top TL = $68^\circ$.
* Contradiction again.
* Let's re-evaluate the position of the $112^\circ$ at the top.
* Maybe it is Top-Right? No, it's on the left.
* Maybe the Bottom-Left $68$ is actually Top-Left (Interior)?
* If Bottom TL (Interior) = $68$, then Top TL (Exterior) corresponds to it? No.
* Let's look at Consecutive Interior Angles.
* If Top TL = $112$, then Top TR = $68$.
* If Lines are Parallel:
* Top TR ($68$) corresponds to Bottom TR. So Bottom TR = $68$.
* Top TL ($112$) corresponds to Bottom TL. So Bottom TL = $112$.
* Let's check the bottom labels in Diagram 6.
* Left label: $68^\circ$. Position: Below C, Left of Trans (Bottom-Left).
* Right label: $68^\circ$. Position: Below D, Right of Trans (Bottom-Right)?
* If Bottom-Left = $68$ and Bottom-Right = $68$, impossible.
* Maybe the Right label is Top-Right (Above D, Right of Trans)?
* If Bottom-Left = $68$ and Top-Right = $68$, they are vertical. Consistent.
* But this implies Bottom TL = $68$.
* And we know Top TL = $112$.
* Corresponding angles: Top TL ($112$) should equal Bottom TL ($68$). They don't.
* Is it possible the transversal is not a straight line? No.
* Is it possible the lines are not parallel? The title says "Corresponding Angles", implying parallel lines properties.
* Let's look at the label $112$ again. Is it Top-Right?
* The arc is on the left side of the transversal.
* Is it possible the Bottom-Left $68$ is actually Bottom-Right?
* No, it's on the left.
* Let's try one more interpretation: Alternate Interior Angles.
* Top Left ($112$) is Exterior.
* Bottom Right ($68$) is Exterior.
* Top Right ($68$) is Exterior.
* Bottom Left ($68$) is Exterior.
* If Top Left = $112$, then Bottom Left (Corresponding) = $112$.
* The diagram labels Bottom Left as $68$.
* $112 + 68 = 180$.
* These are Consecutive Interior? No.
* These are Linear Pair on the transversal? No.
* Wait. Look at Diagram 6 Top. $112^\circ$.
* Look at Diagram 6 Bottom Left. $68^\circ$.
* $112 + 68 = 180$.
* These are Consecutive Interior Angles if one is interior and one is interior?
* Top $112$ is Top-Left (Exterior).
* Bottom $68$ is Bottom-Left (Exterior).
* They are on the same side.
* If lines are parallel, Consecutive Exterior Angles are supplementary?
* Yes. Same-Side Exterior Angles are supplementary.
* So the diagram is consistent with parallel lines.
* Task: Find the corresponding angle measurements.
* Corresponding Angle to Top-Left ($112$) is Bottom-Left.
* Bottom-Left is given as $68$? No, that violates "Corresponding Angles are Equal".
* Corresponding Angles are EQUAL.
* If Top-Left is $112$, Bottom-Left MUST be $112$.
* The diagram shows $68$ there.
* Therefore, the angle labeled $68$ is NOT the corresponding angle.
* The corresponding angle to Top-Left ($112$) is the angle in the Bottom-Left position.
* The angle in the Bottom-Left position is $112^\circ$.
* The angle labeled $68^\circ$ is the supplement.
* So, for Diagram 6:
* Top TL = $112^\circ$.
* Corresponding Bottom TL = $112^\circ$.
* Top TR = $68^\circ$.
* Corresponding Bottom TR = $68^\circ$.
* The labels in the diagram ($68$ at bottom left) might be indicating the vertical angle to the interior?
* Regardless, the question asks for the corresponding angle measurements.
* So, if Top is $112$, Corresponding is $112$.
* If Top is $68$ (TR), Corresponding is $68$.

Final Plan:
For each diagram, I will state the measures of the angles at the circled intersection, ensuring they correspond to the angles at the other intersection.

Diagram 1:
Top: $134, 46$.
Bottom (Circle): Corresponds to Top.
TL: $134^\circ$. TR: $46^\circ$. BL: $46^\circ$. BR: $134^\circ$.

Diagram 2:
Bottom: $75$ (TL), $105$ (TR), $75$ (BL).
Top (Circle): Corresponds to Bottom.
TL: $75^\circ$. TR: $105^\circ$. BL: $75^\circ$. BR: $105^\circ$.

Diagram 3:
Bottom: $31^\circ$ (TL).
Top (Circle): Corresponds to Bottom.
TL: $31^\circ$. TR: $149^\circ$. BL: $149^\circ$. BR: $31^\circ$.

Diagram 4:
All filled.
Top: $137, 43$.
Bottom: $43, 137$.
Correspondences:
Top TL ($137$) corresponds to Bottom TL ($137$). (Note: Diagram label $43$ is likely Alternate Interior or I'm misreading position, but mathematically Corresponding TL is $137$).
Actually, looking at Diagram 4 again:
Top Left $137$. Bottom Left $43$.
These are Consecutive Interior? No.
They are Same-Side Interior?
If Top Left is Exterior, Bottom Left is Interior.
Same-Side Interior/Exterior?
Let's just give the values that *should* be there for correspondence.
Top TL ($137$) -> Bottom TL ($137$).
Top TR ($43$) -> Bottom TR ($43$).

Diagram 5:
Bottom: $142^\circ$ (BL).
Top (Circle): Corresponds to Bottom.
BL: $142^\circ$. BR: $38^\circ$? No.
Bottom BL ($142$) corresponds to Top BL ($142$).
So Top BL = $142^\circ$.
Top TL = $38^\circ$ (Supp).
Top TR = $142^\circ$ (Vert to BL? No, Vert to TL is BR. Vert to BL is TR).
Top TR = $38^\circ$? No.
Vertical to Top BL ($142$) is Top TR? No. Vertical to BL is TR.
So Top TR = $14