A parallelogram has one angle that measures 160°. What are the measures of
the other three angles in the
parallelogram?

Hey there! I'm happy to help!

All of the interior angles of a parallelogram add up to 360 degrees. This is because a parallelogram is basically two triangles, and with triangles the interior angles add up to 180.

Diagonal angles of a parallelogram have the same measure. We have one angle that is 160 degrees, so the angle diagonal to that one is also 160 degrees.

160+160=320

We only have 40 degrees left for the other angles. Since these other angles are diagonal from each other, they will have the same value, so we have to split this 40 up evenly for them.

40/2=20

Therefore, the other three angles of this parallelogram are 160, 30, and 30 degrees.

Have a wonderful day! :D

160°, 20°, and 20°

Step-by-step 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°

b

step-by-step explanation: