Given x || y. from the picture down below

m∠6 = (8x – 13)° and m∠3 = (4x + 1)°. find m∠7.

a. 115°
b. 65°
c. 57°
d. 99°

First we need to find the value of x. Since angles 3 and 6 are equal to 180 (by the Same-Side Angle Theorem) we can set them equal to 180 to find x.

(8x-13)+(4x+1)=180
Simplified is
12x-12=180
Add 12 to both side to get
12x=192
Divide by 12 to get that x=16

Now we can plug this into angle 6 to find its measure.
8(16)-13=?
128-13=115

Then to get angle 7, we subtract this from 180.
180-115=65

So angle 7 is equal to 65 degrees.

:)