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) vertical angles theorem 6) m∠3 + m∠4 = 30 + m∠4 6) addition property of equality 7) m∠4 = 60 7) vertical angles theorem 8) m∠3 + m∠4 = 30+ 8) substitution

Explanation:

Step1: Find m∠1

Given m∠2 = 30 and m∠1 = 2m∠2, substitute m∠2 into the equation for m∠1. So m∠1=2×30 = 60.

Step2: Find m∠3

By the Vertical - Angles Theorem, since ∠2 and ∠3 are vertical angles, m∠3=m∠2 = 30.

Step3: Find m∠4

By the Vertical - Angles Theorem, since ∠1 and ∠4 are vertical angles, m∠4=m∠1 = 60.

Step4: Prove m∠3 + m∠4 = 90

Substitute m∠3 = 30 and m∠4 = 60 into m∠3 + m∠4. We get m∠3 + m∠4=30 + 60=90.

Answer:

The two - column proof is completed as follows:

Statements	Reasons
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) Vertical Angles Theorem
6) m∠3 + m∠4 = 30 + m∠4	6) Addition Property of Equality
7) m∠4 = 60	7) Vertical Angles Theorem
8) m∠3 + m∠4 = 30+60	8) Substitution
9) m∠3 + m∠4 = 90	9) Simplification