Question

write a two - column proof for the following. given: m∠2 = 30, m∠1 = 2m∠2. prove: m∠3 + m∠4 = 90. (do not include the degree symbol in your answers.) statements reasons 1) m∠2 = 30 1) given 2) m∠1 = 2m∠2 2) given 3) m∠1 = 2(30) 3) substitution 4) m∠1 = 60 4) simplification 5) m∠3 = 30 5)

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Since ∠2 and ∠3 are vertical angles, if m∠2 = 30, then m∠3=30.

Step2: Recall linear - pair property

∠1 and ∠4 form a linear - pair. The sum of angles in a linear - pair is 180. Since m∠1 = 60, then m∠4=180 - m∠1 = 180 - 60=120. But we can also use the fact that ∠1 and ∠2 are adjacent angles and ∠3 and ∠4 are adjacent angles, and the sum of all angles around a point is 360. Also, ∠1 and ∠4 are vertical angles to ∠2 and ∠3 respectively. Since ∠2 and ∠3 are vertical angles and ∠1 and ∠4 are vertical angles, and we know m∠2 = 30, m∠1 = 60. ∠3 and ∠4 are complementary because ∠1 and ∠2 are adjacent and ∠3 and ∠4 are adjacent. Since m∠3 = 30 and m∠4 = 60 (because ∠1 and ∠4 are vertical angles and ∠2 and ∠3 are vertical angles), m∠3+m∠4=30 + 60.

Step3: Calculate the sum

m∠3+m∠4=30+60 = 90

Answer:

90