Angle 1 and angle 2 are a linear pair. Measure of angle 1 = x-36, and measure of angle 2 = x+84. Find the measure of each angle.

Linear pair means supplementary so

x-36+x+84=180

2x+48=180

2x=132

x=66

Therefore angle 1 is 30 while angle 2 is 150

Angle1 + angle2 = 180° (because they are a linear pair)

or, (x-36) + (x+84) = 180

or, x - 36 + x + 84 = 180

or, 2x + 48 = 180

or, 2x = 180 - 48

or, 2x = 132

or, x = 132/2

therefore, x = 66

angle1 = (x - 36) = 66-36 = 30°

angle2 = (x+84) = 66 + 84 = 150°