Question

In the trapezoid below, if < BAC = 103 °, what is the measure of < DCA.

Answer 1

A trapezoid has the angles on either side of the bases with the same measure.

Then,

∠BAC = ∠DBA

and

∠DCA = ∠BDC

Also, adjacent sides are supplementary. This means that their measures add up to 180 degrees.

Then,

∠BAC + ∠DCA = 180

Replace using the given values:

103 + ∠DCA = 180

Solve for ∠DCA:

∠DCA = 180 - 103

∠DCA = 77

Hence, the correct answer is option D