Question

In parallelogram ABCD, the measure of angle A is 99 degrees. Explain why the
measure of adjacent angle B must be 81 degrees.

Answer 1

Answer:

The measure of angle B must be 81° because angles A and B are interior supplementary angles

Step-by-step explanation:

Let us revise the properties of a parallelogram

In any parallelogram:

• Every two opposite sides are parallel

• Every two opposite sides are equal in length

• Every two opposite angles are equal in measure

• Every to adjacent angles are interior supplementary angles

Let us solve our question

In parallelogram ABCD

∵ AD and BC are opposite sides

∴ AD // BC

∵ ∠A and ∠B are adjacent angles

→ That means ∠A and ∠B are interior supplementary angles

∴ ∠A and ∠B are supplementary angles

∵ The sum of the measures of the supplementary angles is 180°

∴ m∠A + m∠B = 180°

∵ m∠A = 99°

∴ 99° + m∠B = 180°

→ Subtract 99° from both sides

∴ 99° - 99° + m∠B = 180° - 99°

∴ m∠B = 81°

The measure of angle B must be 81° because angles A and B are interior supplementary angles