The trapezoid ABCD has angle C=70 degrees and D=50 degrees. Find the size of angle A and angle B

Angle A = 130° and Angle B = 110°

Solution:

Given ABCD is a trapezoid with ∠C = 70° and ∠D = 50°

If ABCD is a trapezoid, then AB is parallel to CD.

AD is a transversal to AB and CD and

BC is a tranversal to AB ad CD.

Sum of the interior angles on the same side are supplementary.

∠A + ∠D = 180°

⇒ ∠A + 50° = 180°

Subtract 50° on both sides to equal the expression.

⇒ ∠A = 180° - 50°

⇒ ∠A = 130°

Similary, ∠B + ∠C = 180°

⇒ ∠B + 70° = 180°

Subtract 50° on both sides to equal the expression.

⇒ ∠B = 180° - 70°

⇒ ∠B = 110°

Hence, angle A = 130° and angle B = 110°.