Answer:
x = 20
y = 25
Explanation:
Vertical angles are always congruent, that is a theorem.
Set the vertical pairs equal to each other.
182 - 4x = 5x + 2
The lowest of the two coefficients is 4x, so that will be added to both sides.
4x + 5x = 9x
Simplify
9x + 2 = 182
Subtract both sides by 2
9x = 180
Divide by 9
180/9 = 20
x = 20
Plug in the 20 to get the angle measure.
182 - 80 = 102
the vertical pairs are 102 degrees
There is another theorem that sets the two angles outside as congruent.
So set 4y + 2 = 102
Subtract 2
100
Divide 4, which equals 25
y = 25