In the given figure, AB ∥ CD. If the complement of ∠5 equals the supplement of ∠4, find the measures of ∠4 and ∠5.

Angle 4 = 135, angle 5 = 45

Step-by-step explanation:

Consecutive interior angles are supplementary, therefore angle 5 + angle 8 = 180 degrees. Since the complement of 5 is the supplement of 4, we can write the system of equations.

180 - x = 90 - y or -x + y - 90 - 180 or -x + y = -90 or x - y = 90

x + y = 180

x - y = 90

Where angle 4 is x and angle 5 is y.

y = 180 - x

x - (180 - x) = 90

x - 180 + x =90

x + x = 270

2x = 270

x = 135

By plugging that in to an equation we can solve for y.

y = 45

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

36

step-by-step explanation: