The measure of one angle of a parallelogram is 80°. What are the measures of the remaining angles?

Solution:

Given, the measure of one angle of a parallelogram is 80 degrees.

We have to find the measure of the remaining angles.

From the properties of a parallelogram,

The opposite angles are congruent.

The consecutive angles are supplementary.

Let the measure of Angle A = 80°

A and C are opposite angles.

∠A = ∠C

So, ∠C = 80°

A and D are consecutive angles.

∠A + ∠D = 180°

80° + ∠D = 180°

∠D = 180° - 80°

∠D = 100°

D and B are opposite angles.

∠D = ∠B

So, ∠B = 100°

Therefore, the measures of the remaining angles are 100°, 80°, and 100°.

The measure of one angle of a parallelogram is 80∘. What are the measures of the remaining angles?

Summary:

The measure of one angle of a parallelogram is 80°. The measures of the remaining angles are 100°, 80°, and 100°.