In parallelogram ABCD, the measure of interior angle A is 72^\circ. What is the measure, i… — ACT

In parallelogram $ABCD$ , the measure of interior angle $A$ is $72^\circ$ . What is the measure, in degrees, of interior angle $B$ ?

Answer: 108 degrees

The measure of interior angle

B

108

degrees.

In parallelogram

ABCD

, interior angles

A

and

B

are consecutive angles. A fundamental property of parallelograms is that consecutive angles are supplementary (their measures sum to

180^\circ

). Therefore, the measure of angle

B

is calculated as

180^\circ - 72^\circ = 108^\circ

Use the consecutive angles property of parallelograms.

The sum of consecutive interior angles

A

and

B

180^\circ

Since opposite sides of a parallelogram are parallel, consecutive interior angles are supplementary.

Set up the equation and solve for the unknown angle.

m\angle B = 108^\circ

Subtract

72^\circ

from

180^\circ

Properties of parallelograms (consecutive angles are supplementary)

Question