Find the measure of each indicated angle in the given diagrams involving parallel lines and transversals.

Let's solve each of these problems step by step. All the diagrams involve parallel lines cut by a transversal, and we are to find the measure of the indicated angles using angle relationships such as:

- Corresponding angles are equal.
- Alternate interior angles are equal.
- Alternate exterior angles are equal.
- Same-side interior angles are supplementary (add up to 180°).
- Vertical angles are equal.
- Linear pairs add up to 180°.

We’ll go through each one.

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11)

Given: Two parallel lines, transversal forms a 110° angle below the bottom line on the right side. We're to find the angle above the top line on the left side (marked with "?").

- The 110° angle and the unknown angle are corresponding angles (same position relative to the transversal and the parallel lines).
- So, they are equal.

✔ Answer: 110°

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12)

Given: Two parallel lines, transversal forms an 84° angle above the top line on the left side. We’re to find the angle below the bottom line on the right side (marked with "?").

- This is alternate interior or corresponding? Let’s see:
- The 84° angle is above the top line, on the left.
- The unknown angle is below the bottom line, on the right.
- That makes them vertical angles to corresponding angles.
- Actually, let’s trace it:
- The 84° angle has a vertical angle directly opposite it (also 84°), which is below the top line, on the right.
- That vertical angle corresponds to the unknown angle (since both are on the same side of the transversal and between the lines).
- So, the unknown angle is corresponding to the 84° angle → equal.

✔ Answer: 84°

Alternatively: Since the lines are parallel, corresponding angles are equal, and the unknown angle is in the same relative position.

✔ Answer: 84°

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13)

Given: Two parallel lines, transversal forms a 100° angle above the top line on the right side. Unknown angle is below the bottom line on the left side.

- The 100° angle is on the top-right.
- The unknown angle is on the bottom-left.
- These are alternate interior angles? No — alternate interior would be on opposite sides but inside.
- Wait: 100° is outside (above top line), and the unknown is outside (below bottom line) — so they are alternate exterior angles.
- Alternate exterior angles are equal.

✔ Answer: 100°

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14)

Given: Two parallel lines, transversal forms an 111° angle below the bottom line on the right side. Unknown angle is above the top line on the left side.

- The 111° angle is below the bottom line, on the right.
- The unknown is above the top line, on the left.
- These are opposite in direction — this looks like vertical angles or corresponding?

Wait: Think about it:
- The 111° angle is outside, below the bottom line, right side.
- Its vertical angle is also 111°, located above the bottom line, on the right.
- That 111° angle is corresponding to the unknown angle (both are on the left? No — wait).

Actually:
- The 111° angle is on the right, below the bottom line.
- The unknown is on the left, above the top line.
- So they are not corresponding.

But consider: The angle adjacent to 111° on the same side of the transversal (on the bottom line) is 180° - 111° = 69° (linear pair).
- That 69° angle is interior, on the right side, between the lines.
- Then, its corresponding angle is on the top line, right side, between the lines → also 69°.
- But the unknown is on the left side, above the top line — that's vertical to the 69°?

Wait — better approach:

The 111° angle and the unknown angle are vertical angles to each other? No — they’re not adjacent.

Wait — actually, think about supplementary angles.

But here's a better way: The angle adjacent to 111° (on the bottom line) is 69° (because 180° - 111° = 69°). That 69° angle is between the lines, on the right side.

Then, the corresponding angle on the top line, right side, is also 69°.

Now, the unknown angle is above the top line, on the left side.

Wait — maybe it's alternate exterior?

Let’s label:

- The 111° angle is exterior, on the bottom-right.
- The unknown is exterior, on the top-left.
- So they are opposite — alternate exterior angles?

Yes! Alternate exterior angles are on opposite sides of the transversal and outside the parallel lines.

So: Top-left and bottom-right → yes, alternate exterior → equal.

✔ So, 111°

✔ Answer: 111°

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15)

Given: Two parallel lines, transversal forms a 125° angle above the top line on the left side. Unknown angle is below the bottom line on the right side.

- 125° is above top line, left side → exterior
- Unknown is below bottom line, right side → exterior
- Are they alternate exterior? Yes: one on left, one on right; both outside.
- And since they are on opposite sides of the transversal → alternate exterior angles → equal

✔ Answer: 125°

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16)

Given: Two parallel lines, transversal forms a 47° angle below the bottom line on the left side. Unknown angle is above the top line on the right side.

- 47° is below bottom line, left → exterior, left
- Unknown is above top line, right → exterior, right
- Opposite sides → alternate exterior angles → equal

✔ Answer: 47°

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17)

Given: Two parallel lines, transversal forms a 53° angle above the top line on the right side. Unknown angle is below the bottom line on the left side.

- 53° is above top line, right → exterior
- Unknown is below bottom line, left → exterior
- On opposite sides → alternate exterior angles → equal

✔ Answer: 53°

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18)

Given: Two parallel lines, transversal forms a 113° angle below the bottom line on the left side. Unknown angle is above the top line on the right side.

- 113° is below bottom line, left → exterior, left
- Unknown is above top line, right → exterior, right
- Opposite sides → alternate exterior angles → equal

✔ Answer: 113°

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 11) | 110° |
| 12) | 84° |
| 13) | 100° |
| 14) | 111° |
| 15) | 125° |
| 16) | 47° |
| 17) | 53° |
| 18) | 113° |

All solved using angle relationships in parallel lines cut by a transversal.

Let me know if you'd like a diagram explanation!