ABCD is a parallelogram with diagonal AC. If the measure of angle DCA is 26° and the measure of angle ABC is 113°, what is the measure of angle BCA?
Parallelogram ABCD with diagonal AC; the measure of angle ABC is 113 degrees, and the measure of angle DCA is 26 degrees.
26°
41°
52°
67°
Since ABCD is a parallelogram, opposite angles are equal. Therefore, angle ADC is also 113 degrees.
In triangle ADC, the sum of the angles is 180 degrees. So, angle DCA + angle ADC + angle CAD = 180 degrees.
26 + 113 + CAD = 180
CAD = 41 degrees
Since BCA is the same as CAD, the measure of angle BCA is 41 degrees.
Therefore, the correct answer is 41°.