Question

Sasha sketches a proof of the theorem that vertical angles are congruent. She uses the diagram below. image 60e77c675d4148c2bd12b955d853b377 Angle 1 is supplementary to angle 2. Angle 3 is supplementary to angle 2. By the transitive property of equality, the measure of angle 1 is equal to the measure of angle 3. Angles 1 and 3 are congruent. All vertical angles are congruent. Which expression represents the measure of both angle 1 and angle 3? A 2⋅m∠2 B 90°+m∠2 C 180°−m∠1 D 180°−m∠2

Answer 1

Answer:

Option D (180°-m∠2)

Step-by-step explanation:

we know that

m∠1+m∠2=180° ------> equation A (by supplementary angles)

m∠3+m∠2=180° ------> equation B (by supplementary angles)

m∠1=m∠3 -----> equation C (by vertical angles)

Solve for m∠1 in equation A

m∠1=180°-m∠2

Remember that

m∠1=m∠3

so

m∠3=180°-m∠2

therefore

m∠1=180°-m∠2

m∠3=180°-m∠2

The expression that represent the measure of both angle 1 and angle 3 is

(180°-m∠2)