The following is a special trapezoid. Given AB || DC and m∠A = 113° Find the measure of ∠D.

67°

77°

113°

123°

The answer is 67°.

Since the parallel sides of a trapezoid are called bases, the bases in our given trapezoid are AB and DC. We know that the corresponding pairs of base angles, such as ∠A and ∠D, or ∠B and ∠C, are supplementary, therefore, their angles add up to 180 degrees:

∠A + ∠D = 180°

∠B + ∠C = 180°

Given that m∠A = 113°, we can calculate for the measure of ∠D:

113° + ∠D = 180°

∠D = 180° - 113° = 67°