Question

If the measure of angle 2 is (5 x + 14) degrees and angle 3 is (7 x minus 14) degrees, what is the measure of angle 1 in degrees?

2 lines intersect to form 4 angles. From top left, clockwise, the angles are 1, 2, 3, 4.
88 degrees
89 degrees
90 degrees
91 degrees

Answer 1

Angle 2 and angle 3 are adjacent on a straight line, so they are supplementary:
(5x + 14) + (7x − 14) = 180
12x = 180
x = 15

Angle 3 = 7(15) − 14 = 105 − 14 = 91°. Angle 1 is vertical to angle 3, so angle 1 = 91°.