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() 3) substitution

Explanation:

Step1: Find the measure of ∠1

Since \(m\angle2 = 30\) and \(m\angle1=2m\angle2\), by substitution, \(m\angle1 = 2\times30=60\).

Step2: Use vertical - angle property

\(\angle1\) and \(\angle3\) are vertical angles, so \(m\angle1=m\angle3 = 60\) (vertical angles are equal).
\(\angle2\) and \(\angle4\) are vertical angles, so \(m\angle2=m\angle4 = 30\) (vertical angles are equal).

Step3: Calculate \(m\angle3 + m\angle4\)

\(m\angle3 + m\angle4=60 + 30=90\).

Answer:

The proof is completed as above. The steps in the two - column proof would be:

Statements	Reasons
2) \(m\angle1 = 2m\angle2\)	2) Given
3) \(m\angle1=2\times30\)	3) Substitution
4) \(m\angle1 = 60\)	4) Simplification
5) \(m\angle3=m\angle1\)	5) Vertical angles are equal
6) \(m\angle3 = 60\)	6) Substitution (from 4 and 5)
7) \(m\angle4=m\angle2\)	7) Vertical angles are equal
8) \(m\angle4 = 30\)	8) Substitution (from 1 and 7)
9) \(m\angle3 + m\angle4=60 + 30\)	9) Addition property of equality
10) \(m\angle3 + m\angle4 = 90\)	10) Simplification