Line AB is perpendicular to line BC. Point E is in the interior of angle ABC. If angle ABE = 2x+3 and angle EBC = 4x-9, find x. Then find the measure of both angles.

1 answer

Their sum must equal 90°

2x+3 + 4x-9 = 90
6x = 96
x = 16

one angle is 2(16)+3 or 35°
the other is 4(16)-9 or 55°

(notice 35+55=90)