Question

You do not need to show all of your work for this one. But be sure that you can prove your answer is correct!

Answer 1

Quick answer :

`\color{plum}m∠ABC = 71°`

Steps to derive the correct answer :

• Opposite angles of a parallelogram are equal.
• Angles on the same side are supplementary.

Which means :

m∠ABC = ∠ADC (opposite angles of a parallelogram)

m∠ABC :

= 37° + 34°

= 71°

Thus, the measure of ∠ABC = 71°

Let us find the measures of the other angles as well :

m∠BCD + m∠ADC = 180°

m∠BCD + 71 = 180°

m∠BCD = 180 - 71

m∠BCD = 109°

Thus, the measure of∠BCD = 109°

m∠BCD = ∠BAD (opposite angles of a parallelogram)

m∠BAD = 109°

Thus, the measure of ∠BAD = 109°

Therefore, m∠ABC = 71°

Answer 2

• 109°

Explanation:

Given isosceles trapezoid AB = CD

Angles B and C are congruent and angles A and D are congruent.

A and B, as well as C and D sum to 180 as supplementary angles, therefore:

• m∠ABC = 180° - ∠A = 180 - ∠D = 180° - (34°+37°) = 180° - 71° = 109°