Question

(do not include the degree symbol in your answers.)
statements\treasons

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

Explanation:

Step1: Recall previous values

We know from step 8 that we need to simplify $30 + 60$.

Step2: Perform addition

$30+60 = 90$

Answer:

90