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A parallelogram has one angle that

measures 160°. What are the measures of
the other three angles in the
parallelogram?

1 Answer

1 vote

Answer:

160°, 20°, and 20°

Explanation:

The sum of the measures of the interior angles of a polygon of n sides is

(n - 2)180.

A parallelogram has 4 sides and 2 pairs of congruent opposite angles.

The sum of the measures of the interior angles of a parallelogram is:

(n - 2)180 = (4 - 2)180 = 2(180) = 360

Let each angle of one pair of opposite angle measure x, and let each angle of the other pair of opposite angles measure y.

Then

2x + 2y = 360

We are given that x = 160

2(160) + 2y = 360

320 + 2y = 360

2y = 40

y = 20

The other three angles measure 160°, 20°, and 20°

User Andriej
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