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.

You need to explain WHY you set up your equations the way you did to solve, ie if angles are vertical, supplementary, complementary, etc.

Also include the equations you used to find the missing values.

Answer 1

(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

Answer 2

∠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°