You're given 8 geometry problems (11–18) involving angles formed by a transversal intersecting two lines — often parallel, as indicated by the arrow markings on the lines.
We’ll solve each one using key angle relationships:
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Vertical Angles — equal
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Corresponding Angles — equal if lines are parallel
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Alternate Interior Angles — equal if lines are parallel
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Alternate Exterior Angles — equal if lines are parallel
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Consecutive Interior Angles (Same-Side Interior) — supplementary (add to 180°) if lines are parallel
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Linear Pair — adjacent angles that form a straight line → sum to 180°
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🔢 Problem 11:
Two lines intersect. One angle is 110°, and we’re asked for the angle marked “?” which is
vertically opposite to the 110° angle.
✔ Answer: 110°
> *Vertical angles are congruent.*
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🔢 Problem 12:
Two parallel lines cut by a transversal. The top left angle is 84°. The “?” is the
corresponding angle at the bottom right.
✔ Answer: 84°
> *Corresponding angles are equal when lines are parallel.*
*(Note: You could also say it’s vertically opposite to the corresponding angle, but directly, it’s corresponding.)*
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🔢 Problem 13:
Two parallel lines cut by a transversal. Top left angle = 100°. The “?” is at the bottom right — this is the
alternate interior angle to the 100° angle.
✔ Answer: 100°
> *Alternate interior angles are equal when lines are parallel.*
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🔢 Problem 14:
Parallel lines. Bottom right angle = 111°. The “?” is at the top left — this is the
alternate exterior angle to 111°.
✔ Answer: 111°
> *Alternate exterior angles are equal when lines are parallel.*
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🔢 Problem 15:
Parallel lines. Top left angle = 125°. The “?” is at the bottom right — this is the
corresponding angle.
✔ Answer: 125°
> *Corresponding angles are equal.*
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🔢 Problem 16:
Parallel lines. Bottom left angle = 47°. The “?” is at the top right — this is the
alternate exterior angle.
✔ Answer: 47°
> *Alternate exterior angles are equal.*
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🔢 Problem 17:
Parallel lines. Top left angle = 53°. The “?” is at the bottom left — this is the
same-side interior angle (consecutive interior), so it’s
supplementary to 53°.
✔ Answer: 180° - 53° = 127°
> *Same-side interior angles add to 180° when lines are parallel.*
---
🔢 Problem 18:
Parallel lines. Bottom left angle = 113°. The “?” is at the top right — this is the
alternate exterior angle.
✔ Answer: 113°
> *Alternate exterior angles are equal.*
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✔ Final Answers:
| Problem | Answer |
|---------|--------|
| 11 |
110° |
| 12 |
84° |
| 13 |
100° |
| 14 |
111° |
| 15 |
125° |
| 16 |
47° |
| 17 |
127° |
| 18 |
113° |
All solutions rely on properties of parallel lines cut by a transversal, or vertical angles. Let me know if you’d like diagrams explained further!
Parent Tip: Review the logic above to help your child master the concept of find the measure of each angle indicated worksheet.
