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\treasons

1. ( mangle2 = 30 )\t1) given
2. ( mangle1 = 2mangle2 )\t2) given
3. ( mangle1 = 2(30) )\t3) substitution
4. ( mangle1 = 60 )\t4) simplification
5. ( mangle3 = 30 )\t5) vertical angles theorem
6. ( mangle3 + mangle4 = 30 + mangle4 )\t6) addition property of equality
7. ( mangle4 = 60 )\t7) vertical angles theorem
8. ( mangle3 + mangle4 = 30 + 60 )\t8) substitution
9. ( mangle3 + mangle4 = square )\t9) simplification

Explanation:

Step1: Analyze Statement 8

From statement 8, we have \( m\angle3 + m\angle4 = 30 + 60 \).

Step2: Simplify the sum

To find the value of \( 30 + 60 \), we perform the addition: \( 30+60 = 90 \).

Answer:

90