This is a geometry worksheet about parallel lines and transversals. To solve the problems, I need to apply the rules for angles formed when a transversal crosses two parallel lines.
The key angle relationships are:
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Corresponding angles are equal.
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Alternate interior angles are equal.
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Alternate exterior angles are equal.
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Consecutive interior angles (same-side interior) are supplementary (add up to 180°).
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Vertically opposite angles are equal.
I will solve each problem one by one.
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Problem 1
- We are given that Line A and Line B are parallel, and Line C is a transversal.
- The diagram shows an angle of 85°. This angle is adjacent to Angle 1 on line A, forming a straight line (linear pair). Therefore, they are supplementary.
- So, Angle 1 = 180° - 85° = 95°.
- Angle 2 is vertically opposite to the 85° angle, so Angle 2 = 85°.
Answer for Problem 1:
- Angle 1 = 95°
- Angle 2 = 85°
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Problem 2
- The given angle is 122°. This angle is adjacent to Angle 1 on line A, forming a linear pair.
- So, Angle 1 = 180° - 122° = 58°.
- Angle 2 is vertically opposite to the 122° angle, so Angle 2 = 122°.
Answer for Problem 2:
- Angle 1 = 58°
- Angle 2 = 122°
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Problem 3
- The given angle is 72°. This angle is adjacent to Angle 1 on line A, forming a linear pair.
- So, Angle 1 = 180° - 72° = 108°.
- Angle 2 is vertically opposite to the 72° angle, so Angle 2 = 72°.
Answer for Problem 3:
- Angle 1 = 108°
- Angle 2 = 72°
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Problem 4
- The given angle is 140°. This angle is adjacent to Angle 2 on line B, forming a linear pair.
- So, Angle 2 = 180° - 140° = 40°.
- Angle 1 is vertically opposite to the 140° angle, so Angle 1 = 140°.
Answer for Problem 4:
- Angle 1 = 140°
- Angle 2 = 40°
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Final Answers:
1. Angle 1 = 95°, Angle 2 = 85°
2. Angle 1 = 58°, Angle 2 = 122°
3. Angle 1 = 108°, Angle 2 = 72°
4. Angle 1 = 140°, Angle 2 = 40°
Parent Tip: Review the logic above to help your child master the concept of transversals and parallel lines worksheet.
