Question

write a two - column proof for the following.
given: ( mangle2 = 30 )
( mangle1 = 2mangle2 )
prove: ( mangle3 + mangle4 = 90 )
(do not include the degree symbol in your answers.)
statements\t\t\t\t\treasons

1. ( mangle2 = 30 )\t\t\t1) given
2. ( mangle1 = 2mangle2 )\t\t2) given
3. ( mangle1 = 2square )\t\t3) substitution

Explanation:

Step1: Identify the value to substitute

We know from statement 1 that \( m\angle2 = 30 \). In statement 2, \( m\angle1 = 2m\angle2 \). So we substitute the value of \( m\angle2 \) into the equation for \( m\angle1 \).

Step2: Substitute the value

Substitute \( m\angle2 = 30 \) into \( m\angle1 = 2m\angle2 \), we get \( m\angle1 = 2\times30 \). So the blank in statement 3 should be filled with 30.

Answer:

30