One angle is eight times it's supplement increased by 45 degrees. What is the measures of the two supplementary angles?

Angle 1 = 8x + 45

Angle 2 = x

x + 8x + 45 = 180

combine like terms

9x + 45 = 180

subtract 45 from both sides

9x = 135

divide both sides by 9 to isolate x

x = 15

Angle 1 = 8 (15) + 45 = 165 degrees

Angle 2 = 15 degrees