Question

Use the given information to find the values of x and y. Then also find the measures of all four angles in this figure.

Answer 1

∠1 = ∠3  [vertical angles]
5x - 20 = 3x + 8
5x - 3x = 8 + 20
2x = 28
x = 14
m∠1 = 3x + 8 = 3*14 + 8 = 50°
m∠3 = m∠1 = 50°

∠1 + ∠2 = 180°    [supplementary angles]
m∠2 = 180 - m∠1 = 180 - 50 = 130°

m∠4 = m∠2 = 130°   [vertical angles]

(5x + 4y) = 130     [x = 14]
5*14 + 4y = 130
70 + 4y = 130
4y = 130 - 70
4y = 60
y = 60/4
y = 15

Answer:
x = 14
y = 15
m∠1= 50°
m∠2= 130°
m∠3= 50°
m∠4= 130°

Answer 2

(3x+8)=(5x-20). The angles are vertical so it's equal. You then used the solved for x to solve (3x+8)+(5x+4y)=180 to solve for y. This is because these two angles are supplementary so they add to 180. We assume x is already known from the first equation. 

Solving the first equation:
2x=28
x=14

Second equation: 3*14+8+5*14+4y=180
42+8+70+4y=180
4y=180-120
4y=60
y=15