Help finding the measure of each angle.?

Question

Given AB(line) || DC(line), m∠1 = 112, m∠2 = 4x, and m∠3 = 3x + 12, find the measure of each angle below.

1. ∠2
2. ∠3
3. ∠D

Answer 1

Observe that

m∠1+m∠2+m∠3=180

Substitute 112 for m∠1,4x for m∠2 and 3x+12 for m∠3

112+4x+3x+12=180

7x+124=180

7x=56

x=8

------------------------

1.

Calculate the m∠2

m∠2=4x

         =4*8

         =32

 

2.

m∠3=3x+12

         =3*8+12

         =36

 

3.

Corresponding angles are equal.

∠D=∠1

      =112