Question

date: 1. give all relationships between ∠1 and ∠2. 2. 3. ∠1 and ∠2 are vertical angles. if m∠1 = 64°, find m∠2. 4. ∠q and ∠r are complementary angles. if m∠r = 73°, find m∠q. 5. in the diagram to the left, if m∠aed = 152°, find each angle measure: a) m∠aec b) m∠ceb c) m∠fec

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal.

Step2: Solve for question 1

Since ∠1 and ∠2 are vertical angles, ∠1 = ∠2.

Step3: Solve for question 2

In the right - angled figure, ∠1 and ∠2 are complementary (sum to 90°) as they form a right angle.

Step4: Solve for question 3

Since ∠1 and ∠2 are vertical angles, if m∠1 = 64°, then m∠2=64°.

Step5: Solve for question 4

If ∠Q and ∠R are complementary and m∠R = 73°, then m∠Q=90° - 73° = 17°.

Step6: Solve for question 5

a) ∠AED and ∠BEC are vertical angles. Given m∠AED = 152°, then m∠BEC = 152°. ∠AEC and ∠AED are supplementary (sum to 180°), so m∠AEC=180° - 152° = 28°.
b) m∠CEB = 152° (vertical to ∠AED).
c) ∠FEC and ∠AED are vertical angles, so m∠FEC = 152°.

Answer:

1. ∠1 and ∠2 are vertical angles, so ∠1 = ∠2.
2. ∠1 and ∠2 are complementary (∠1+∠2 = 90°).
3. m∠2 = 64°
4. m∠Q = 17°
5. a) m∠AEC = 28°

b) m∠CEB = 152°
c) m∠FEC = 152°