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: Analyze the substitution

We know from step 1 that \( m\angle2 = 30 \), and from step 2 that \( m\angle1=2m\angle2 \). For the substitution in step 3, we substitute the value of \( m\angle2 \) (which is 30) into the equation for \( m\angle1 \). So we replace \( m\angle2 \) with 30.

Step2: Fill in the blank

So \( m\angle1 = 2\times30 \) (but we don't include the degree symbol as per instruction), so the blank should be filled with 30.

Answer:

30