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 statements. 1) m∠2 = 30 2) m∠1 = 2m∠2 3) m∠1 = 2(30) 4) m∠1 = 60 5) m∠3 = 30

Explanation:

Step1: Find measure of ∠1

Given \(m\angle2 = 30\) and \(m\angle1=2m\angle2\), substitute \(m\angle2\) value. So \(m\angle1 = 2\times30=60\).

Step2: Use vertical - angles property

\(\angle2\) and \(\angle3\) are vertical angles. By the vertical - angles theorem, vertical angles are congruent. So \(m\angle3=m\angle2 = 30\) since \(\angle2\cong\angle3\) (by vertical angles theorem).

Step3: Use linear - pair property

\(\angle1\) and \(\angle4\) are vertical angles. So \(m\angle4=m\angle1 = 60\) since \(\angle1\cong\angle4\) (by vertical angles theorem).

Step4: Calculate \(m\angle3 + m\angle4\)

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

Answer:

The proof is completed as shown above to prove \(m\angle3 + m\angle4 = 90\).