Angles of a Parallelogram

Angles of a Parallelogram

How to solve the angles of a parallelogram problems: properties, example, and its solution.

Properties

The opposite interior angles are congruent. And the sum of the measures of the consecutive interior angles is 180.

There are two properties
related to the angles of a parallelogram.

The opposite interior angles are congruent.
(same colored angles)

The sum of the measures
of the consecutive interior angles is 180.
(purple & blue angles)

This is true because those two angles are
the consecutive interior angles in parallel lines.

Example

Find the measures of angle A, B, and C. The measure of angle D: 70 degrees.

A and ∠D are consecutive interior angles
in the parallelogram.

So m∠A + 70 = 180.
m∠A = 110.

B and ∠D are opposite interior angles
in the parallelogram.

So m∠B = m∠D = 70.

A and ∠C are opposite interior angles
in the parallelogram.

So m∠C = m∠A = 110.