Angle Relationships Worksheet 2 Answer Key - Fill Online ... - Free Printable

Since I can't view or access uploaded images directly, I can’t see the specific diagram or details of your worksheet. However, based on the text you've provided from "Angle Relationships Worksheet #2", I can help you solve it assuming standard geometric configurations typically found in such worksheets.

Let’s go step by step and solve each part using common angle relationships.

---

Part A: Fill in the correct angle

We are given a diagram (not visible) with points labeled:
- Points A, B, C, D, E, F
- Lines intersecting at point X
- Angles formed around point X

Let’s assume that lines AC and BD intersect at point X, forming vertical angles and various supplementary/adjacent pairs. This is typical for such problems.

#### 1) ∠AXE and ________ are vertical angles.
> Vertical angles are opposite angles formed by two intersecting lines.

If ∠AXE is one angle, its vertical angle would be the one directly opposite to it — likely ∠CXD.

✔ Answer: ∠CXD

---

#### 2) ∠AXF and ________ are supplementary angles.
> Supplementary angles add up to 180°. They form a straight line.

If ∠AXF is part of a straight line, then the adjacent angle on the same line would be supplementary.

Assuming ray XF extends to form a straight line with another ray (e.g., XB), then ∠AXB might be the supplement.

But more likely, since we have points like A, X, F — and if F lies on line XD or something similar, let's suppose ∠AXF and ∠FXB make a straight line.

Wait — better assumption: If AX and FX form a straight line through X, then ∠AXF and ∠FXB would be supplementary if B is on the extension.

But without the image, let’s suppose that ∠AXF and ∠FXC are on a straight line? Not clear.

Alternative idea: Common configuration — two lines cross at X: AC and BD. Then:

- ∠AXE and ∠CXD are vertical
- ∠AXF might be a different angle.

Wait — perhaps F is a point on line BD?

Let me re-analyze with standard setup:

Assume:
- Line AC crosses line BD at point X.
- So four angles are formed: ∠AXB, ∠BXC, ∠CXD, ∠DXA
- But also labeled points: A, E, F, etc.

Possibility: Point E is on one side, F on another.

Another common labeling:
- Ray XE and XF may be extensions.

But perhaps this is a three-line intersection or a transversal.

Alternatively, maybe there are rays from X: XA, XB, XC, XD, XE, XF.

But let's look at clue: “∠AXE” — so A and E are endpoints of rays from X.

So likely, several rays originate from X.

But most commonly, in these problems, two lines intersect at X, forming four angles.

Let’s suppose:
- Line AD and line BE intersect at X
- So ∠AXE and ∠CXD are vertical angles → matches question 1

Then:
- ∠AXF: if F is on the same line as D, then ∠AXF and ∠BXF might be supplementary?

Wait — perhaps F is on line CD extended?

This is ambiguous.

But let’s try to deduce from typical problems.

Let’s suppose the following standard diagram:

Two lines intersect at X:
- Line AB passes through X
- Line CD passes through X
- So angles: ∠AXC, ∠CXB, ∠BXD, ∠DXA

But here we have points E and F.

Possibility: E and F are points on the lines.

Maybe:
- E is on ray XD
- F is on ray XB

So:
- ∠AXE = ∠AXD (same angle)
- ∠AXF = ∠AXB

But still unclear.

Wait — perhaps the diagram shows multiple angles at point X with rays XA, XB, XC, XD, XE, XF.

Let’s consider a standard configuration where:
- Two lines intersect at X: say, line AF and line CE
- So they cross at X
- Then vertical angles: ∠AXE and ∠CXF (if E and F are opposite)

But we have ∠AXE mentioned.

Perhaps:
- Ray XA and ray XE form an angle
- Ray XE and ray XF form another
- etc.

Without the image, we need to use logic.

Let’s skip ahead and assume typical answers based on common problems.

---

Let’s try to infer from the questions:

#### 1) ∠AXE and ________ are vertical angles.

Vertical angles are opposite when two lines intersect.

So if ∠AXE is formed by rays XA and XE, then the vertical angle must be formed by the opposite rays.

Suppose line AE and line CF intersect at X.

Then ∠AXE and ∠CXF would be vertical.

But we don’t know F.

Alternatively, suppose:
- Rays XA and XD form one line
- Rays XB and XC form another

Wait — perhaps the diagram has:
- Point X at center
- Rays: XA, XB, XC, XD, XE, XF

Commonly, in such problems:
- ∠AXE and ∠CXD are vertical angles → this is a frequent pattern.

So Answer 1: ∠CXD

✔ 1) ∠CXD

---

#### 2) ∠AXF and ________ are supplementary angles.

Supplementary angles sum to 180°. Often, they form a straight line.

So if ∠AXF is part of a straight line, its supplement is the adjacent angle that completes the line.

For example, if A-X-F is a straight line, then any angle adjacent to ∠AXF along that line would be supplementary.

But ∠AXF is already at X, so likely, ray XF and another ray form a straight line.

Suppose that XF and XB are on a straight line → then ∠AXF and ∠AXB might be supplementary only if A, X, B are colinear.

Wait — perhaps A-X-B is a straight line, and F-X-C is another.

Then ∠AXF and ∠BXF would be supplementary if A-X-B is straight.

But we don’t know.

Alternate idea: Suppose AF is a straight line passing through X.

Then ∠AXF and ∠FXB would be supplementary if B is on the other side.

But again, no clarity.

Let’s think: if ∠AXF and ∠FXB are adjacent and form a straight line, then they are supplementary.

But we need to find which angle is supplementary to ∠AXF.

Common answer: ∠BXF or ∠FXC, but depends.

Wait — perhaps ∠AXF and ∠FXC are on a straight line?

No.

Better approach: Let’s assume the diagram is standard: two lines intersect at X.

Let’s define:
- Line AD intersects line BE at X
- So angles: ∠AXB, ∠BXC, ∠CXD, ∠DXA

But we have E and F.

Wait — perhaps:
- E is on ray XB
- F is on ray XD

Then:
- ∠AXE = ∠AXB (same angle)
- ∠AXF = ∠AXD

Then:
- ∠AXF and ∠FXC? Not helpful.

Alternatively, suppose:
- Ray XA and ray XD form a straight line → so A-X-D is straight
- Ray XB and ray XE form a straight line → B-X-E is straight

Then:
- ∠AXF: if F is on XB, then ∠AXF is between XA and XF (which is XB)
- Then ∠AXF and ∠FXD would be supplementary if A-X-D is straight.

Wait — if A-X-D is straight, then any angle from XA to a ray, and from that ray to XD, adds to 180°.

So if ∠AXF + ∠FXD = 180°, then they are supplementary.

So Answer 2: ∠FXD

But we don’t know.

Alternatively, common answer: ∠BXF or ∠FXC

Wait — perhaps the answer is ∠FXB if F is on the opposite side.

But without diagram, let’s move to easier ones.

---

#### 3) ∠DXC and ________ are complementary angles.

Complementary angles sum to 90°.

So unless specified, this implies one of the angles is 90°, or we're told the measure.

But no measures are given.

So likely, in the diagram, some angles are marked as right angles.

Possibility: ∠DXC is 90°, and we’re to find its complement.

But we don’t know.

Wait — perhaps ∠DXC and ∠CXB are complementary if together they make 90°.

But again, not known.

This suggests that the diagram includes a right angle.

Let’s assume that one of the angles is 90°, and we need to identify its complement.

But without values, hard.

Wait — perhaps the diagram shows perpendicular lines.

Suppose lines AC and BD are perpendicular, intersecting at X.

Then all angles are 90°.

Then every angle is 90°, so no complement unless we’re talking about parts.

But complementary means sum to 90°.

So if ∠DXC = 90°, then its complement is 0° — impossible.

So ∠DXC cannot be 90°.

So likely, ∠DXC is not 90°, but is part of a 90° angle.

For example, if ∠DXC and ∠CXB are adjacent and together form a right angle, then they are complementary.

But we need to guess.

Let’s skip and come back.

---

#### 4) ________ and ________ are adjacent angles.

Adjacent angles share a common vertex and side, but do not overlap.

Any two angles sharing a ray.

Example: ∠AXE and ∠EXB

Or ∠AXB and ∠BXC

So possible answer: ∠AXE and ∠EXB

But we don’t know labels.

Common pair: ∠AXE and ∠EXF

But again, depends.

Let’s assume: ∠AXB and ∠BXC

But we need to pick from diagram.

Typical answer: ∠AXE and ∠EXB

But without diagram, best guess: ∠AXB and ∠BXC

But let’s wait.

---

#### 5) ________ and ∠CXD are supplementary angles.

Supplementary → sum to 180°.

If ∠CXD is one angle, its supplement is the angle that forms a straight line with it.

If C-X-D is a straight line, then any angle from C to X to D is 180°.

But ∠CXD is at X, so if C-X-D is straight, then ∠CXD = 180°, which is degenerate.

More likely, ∠CXD is less than 180°, and its supplement is the adjacent angle on the straight line.

For example, if C-X-A is a straight line, then ∠CXD and ∠DXA might be supplementary.

Wait — if C-X-A is straight, then ∠CXA = 180°, so ∠CXD + ∠DXA = 180°.

So ∠DXA is the supplement.

But we have point E and F.

Alternatively, if D-X-B is straight, then ∠CXD and ∠CXB are supplementary.

So possible: ∠CXB

But again, depends.

But in many diagrams, ∠CXD and ∠AXC are vertical, and ∠AXC and ∠CXD are adjacent and supplementary if A-X-D is straight.

Wait — if A-X-D is a straight line, then ∠AXC and ∠CXD are supplementary.

Yes!

So if A-X-D is straight, then ∠AXC + ∠CXD = 180°

So Answer 5: ∠AXC

✔ 5) ∠AXC

---

#### 6) ________ and ∠AXC are vertical angles.

Vertical angles are opposite.

So if ∠AXC is formed by rays XA and XC, then the vertical angle is formed by the opposite rays.

So if XA and XD are opposite, and XC and XB are opposite, then ∠AXC and ∠DXB are vertical.

So Answer 6: ∠DXB

✔ 6) ∠DXB

Now going back:

From 1) ∠AXE and ∠CXD are vertical → so if ∠AXE and ∠CXD are vertical, then rays XA and XC are opposite, and XE and XD are opposite.

So likely, XA and XC are opposite, so A-X-C is straight.

XE and XD are opposite, so E-X-D is straight.

So lines AC and ED intersect at X.

Then:

- Vertical angles:
- ∠AXE and ∠CXD
- ∠AED and ∠CXE? Wait.

Wait — if lines AC and ED intersect at X, then:
- ∠AXE and ∠CXD are vertical
- ∠A XD and ∠C XE are vertical

So yes.

Then:
- ∠AXF: what is F?

F might be on ray XB or something.

But let’s now fill in what we can.

---

Summary of Part A (based on deduction):

1) ∠AXE and ∠CXD are vertical angles. ✔
2) ∠AXF and ∠FXB are supplementary angles. (Assume F is on line XB, and A-X-B is straight)
But wait — if A-X-B is straight, then ∠AXF and ∠FXB are adjacent and form straight line → supplementary.
So if F is between A and B, then yes.
But more likely, F is on a different ray.

Wait — perhaps F is on ray XD.

Then ∠AXF is between XA and XF (XD), and if A-X-D is straight, then ∠AXF and ∠FXD are parts.

But we need supplement.

Suppose ∠AXF and ∠FXC are supplementary? Unlikely.

Alternative: If A-X-D is straight, and F is on ray XB, then ∠AXF and ∠FXD may not be adjacent.

This is too ambiguous.

But from earlier:

We have:

- ∠AXE and ∠CXD are vertical → so rays XA and XC are opposite, XE and XD are opposite.

So lines AC and ED intersect at X.

Then:
- ∠AXE and ∠CXD: vertical
- ∠A XD and ∠C XE: vertical

Now, what is ∠AXF?

F is probably on ray XB.

But not defined.

Wait — perhaps F is on ray XB, and B is on line EC.

Then ∠AXF is between XA and XF (XB).

Then its supplement could be ∠FXC if A-X-C is straight.

But A-X-C is straight (since XA and XC are opposite), so ∠AXF + ∠FXC = 180° if F is on the same side.

But ∠AXF and ∠FXC share ray XF, and if A-X-C is straight, then yes.

So if A-X-C is straight, and F is on ray XB, then ∠AXF and ∠FXC are adjacent and form straight line → supplementary.

So Answer 2: ∠FXC

But we don’t know.

Alternatively, if ∠AXF and ∠BXF are on a straight line, but unlikely.

Let’s look at question 3: ∠DXC and ________ are complementary.

Complementary → sum to 90°.

So likely, ∠DXC is not 90°, but is part of a right angle.

Suppose that ∠DXC and ∠CXB are complementary, meaning their sum is 90°.

Then Answer 3: ∠CXB

But without measure, hard.

Unless the diagram shows a right angle at X.

Suppose that lines AC and BD are perpendicular, intersecting at X.

Then all angles are 90°.

Then any two adjacent angles are supplementary (sum to 180°), and no two angles are complementary unless one is 0°.

So that can't be.

So likely, only one angle is 90°.

Suppose ∠AXE = 90°, then its complement is 0° — no.

So perhaps ∠DXC is acute, and its complement is another acute angle.

But without info, impossible.

Wait — perhaps the diagram shows a right angle between certain rays.

But let’s skip and go to Part B.

---

Part B: Fill in the correct angle measurement

7) What is the complement of an 11° angle?

Complement = 90° - 11° = 79°

✔ 7) 79°

8) What is the supplement of a 45° angle?

Supplement = 180° - 45° = 135°

✔ 8) 135°

9) What is the complement of a 58° angle?

90° - 58° = 32°

✔ 9) 32°

10) Use the diagram to the right to find m∠2.

You said: "Use the diagram to the right"

But I can’t see it.

However, you wrote: "m∠2 = ____" and "m∠3 = ____", "m∠4 = ____"

And you mention "the diagram to the right" — likely a transversal cutting parallel lines.

Common problem: two parallel lines cut by a transversal.

Angles labeled 1, 2, 3, 4.

Typically:
- ∠1 and ∠2 are adjacent or vertical
- Or ∠1 and ∠2 are corresponding, alternate interior, etc.

But without diagram, assume a standard configuration.

Suppose:
- Two parallel lines, cut by a transversal
- ∠1 = 120° (given in the text: "10) m∠2 = ____" and earlier says "10) – 12. use the diagram to the right")

Wait — the text says: "10) – 12. use the diagram to the right"

And you wrote: "10) m∠2 = ____"
"11) m∠3 = ____"
"12) m∠4 = ____"

And below that, you have a small diagram: two horizontal lines, with a diagonal line crossing them.

Likely: two parallel lines, transversal.

And angles labeled 1, 2, 3, 4.

Common labeling:
- ∠1 at top-left
- ∠2 at top-right
- ∠3 at bottom-left
- ∠4 at bottom-right

And perhaps ∠1 = 120° (but not stated)

Wait — in your message, you have: "10) – 12. use the diagram to the right"

But no value given.

But in the text, it says: "10) m∠2 = ____" — so likely, ∠1 is given.

But you didn’t include the value.

Wait — in your initial message, after "10) – 12. use the diagram to the right", there’s a small diagram with an arrow and angle markings.

But I can’t see it.

However, in many such problems, the first angle is given.

For example, suppose ∠1 = 120°, and it's on the top left.

Then:
- ∠2 is adjacent to ∠1 on the same line → supplementary → 180° - 120° = 60°
- So m∠2 = 60°

Then:
- ∠3 is vertically opposite to ∠1 → so ∠3 = 120°
- ∠4 is vertically opposite to ∠2 → 60°

Or if ∠3 is alternate interior to ∠1, and lines are parallel, then ∠3 = 120°

But without knowing which angles are labeled, hard.

But let’s assume standard labeling:

- ∠1 and ∠2 are on the same side of transversal, adjacent angles → supplementary
- So if ∠1 = 120°, then ∠2 = 60°
- ∠3 is opposite to ∠1 → vertical → 120°
- ∠4 is opposite to ∠2 → 60°

But you didn’t give the measure of any angle.

Wait — in your message, after "10) – 12. use the diagram to the right", there is a small diagram showing:

- Two horizontal lines (parallel)
- A diagonal line crossing them
- An angle marked with a number 1, and a value? No, not visible.

But in the text, you wrote: "10) m∠2 = ____" — so likely, the diagram has ∠1 = 120° or something.

But since you didn’t specify, I can’t compute.

But perhaps in the original image, ∠1 is 120°.

In many textbooks, it’s common.

So assume:
- ∠1 = 120°
- ∠1 and ∠2 are adjacent angles on a straight line → supplementary
- So ∠2 = 180° - 120° = 60°
- ∠3 is vertical to ∠1 → 120°
- ∠4 is vertical to ∠2 → 60°

But ∠3 might be alternate interior to ∠1, so if lines are parallel, ∠3 = 120°

So:

10) m∠2 = 60°
11) m∠3 = 120°
12) m∠4 = 60°

But this is an assumption.

Alternatively, if ∠1 is 60°, then ∠2 = 120°, etc.

But without the diagram, we can’t be sure.

But since you asked to solve, I’ll provide the most likely answers based on common problems.

---

Final Answers (Best Guess Based on Standard Problems):

#### Part A:

1) ∠AXE and ∠CXD are vertical angles.
2) ∠AXF and ∠FXB are supplementary angles. *(assume F is on line XB)*
3) ∠DXC and ∠CXB are complementary angles. *(assume they form 90°)*
4) ∠AXE and ∠EXB are adjacent angles. *(share ray XE)*
5) ∠AXC and ∠CXD are supplementary angles. *(if A-X-D is straight)*
6) ∠DXB and ∠AXC are vertical angles. *(opposite angles)*

#### Part B:

7) Complement of 11° = 79°
8) Supplement of 45° = 135°
9) Complement of 58° = 32°
10) m∠2 = 60° *(assumed ∠1 = 120°)*
11) m∠3 = 120°
12) m∠4 = 60°

---

⚠️ Important Note: These answers are based on typical geometry problems and assumptions about the diagram. To get exact answers, please describe the diagram or upload it again.

If you can describe the diagram (e.g., "two lines intersect at X, with points A, B, C, D, E, F", or "parallel lines with transversal, ∠1 = 120°"), I can refine the answers.

Would you like to describe the diagram?