Question

In a parallelogram ABCD, ∠B = 105°. Determine the measure of ∠A and ∠D.

Answer 1

Given: ∠B = 105°.

We know that the sum of any two successive parallelogram angles is 180°.

∴ ∠A + ∠B = 180°

⇒ ∠A + 105° = 180°

⇒ ∠A = 180° – 105°

= 75°

Also, ∠A + ∠D = 180°

⇒ 75 + ∠D = 180°

⇒ ∠D = 180° – 75°

= 105°

Hence, ∠A = 75° and ∠D = 105°.