Vertical Angles: Definition and Examples

📚 Quick Study Guide

• 📐 Vertical angles are pairs of opposite angles made by intersecting lines.
• ✨ They are always congruent (equal in measure).
• ➕ If one angle is $x$ degrees, the vertical angle is also $x$ degrees.
• 🧭 Vertical angles share a common vertex.
• ✏️ To find the measure of an angle supplementary to a vertical angle, subtract the vertical angle from 180 degrees: $180 - x$.

Practice Quiz

1. Which of the following statements is always true about vertical angles?

   1. They are supplementary.
   2. They are complementary.
   3. They are congruent.
   4. They are right angles.

2. If one vertical angle measures 60°, what is the measure of its vertical angle?

   1. 30°
   2. 60°
   3. 90°
   4. 120°

3. Lines AB and CD intersect at point E. If ∠AEC measures 110°, what does ∠BED measure?

   1. 70°
   2. 90°
   3. 110°
   4. 180°

4. If two intersecting lines form vertical angles and one angle measures 45°, what is the measure of an adjacent angle?

   1. 45°
   2. 90°
   3. 135°
   4. 180°

5. Which pair of angles are vertical angles in the figure below, where lines PQ and RS intersect at point O?

   
   1. ∠POR and ∠ROQ
   2. ∠POS and ∠SOQ
   3. ∠POR and ∠SOQ
   4. ∠POS and ∠POR

6. If ∠1 and ∠3 are vertical angles, and $m∠1 = 3x + 10$ and $m∠3 = 5x - 20$, find the value of x.

   1. 5
   2. 10
   3. 15
   4. 20

7. Two lines intersect, forming angles a, b, c, and d. If angle a is 95 degrees, what is the measurement of angle c, which is vertical to angle a?

   1. 85 degrees
   2. 90 degrees
   3. 95 degrees
   4. 180 degrees