Answer:
m∠B = 53°
Explanation:
You want the measure of the acute angle, given that consecutive interior angles of the trapezoid have measures (32x-1) and (14x-3).
Setup
Consecutive interior angles between the bases of a trapezoid are supplementary:
(32x -1) +(14x -3) = 180
Solution
Simplifying the equation, we get ...
46x -4 = 180
46x = 184 . . . . . . add 4
x = 4 . . . . . . . . divide by 46
The smaller angle is ...
14(4) -3 = 56 -3 = 53
The measure of angle B is 53°.
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Check
The measure of angle C is 32(4) -1 = 127. This is the supplement of the measure of angle B, as it should be.