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.

∠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

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