Question

One angle of a parallelogram measures 20°. What are the measures of the other three angles in the parallelogram?

Answer 1

Answer:

Step-by-step explanation:

Suppose , angle A = 20° ,

=> Angle A = Angle C = 20°

( Opposite angles of IIgm are equal )

*Angle A + Angle D = 90°

=> Angle D = 90°- Angle A

=>Angle D = 90° - 20°

=> Angle D = 70°

* Angle D = Angle B =70°

( Opposite angles of IIgm are equal )

Therefore ,

Angle D =70°

Angle C =20°

Angle B =70°

Answer 2

Answer: The measures of the other two angles in the parallelogram are both 160 degrees.

In a parallelogram, opposite angles are congruent, which means they have the same measure. Therefore, if one angle in a parallelogram measures 20 degrees, then the opposite angle also measures 20 degrees.

The sum of the measures of the angles in a parallelogram is 360 degrees. Since opposite angles are congruent, the other two angles in the parallelogram have the same measure as each other. Let's call the measure of each of these angles x.

So we have:

One angle = 20 degrees

Opposite angle = 20 degrees

Two other angles = x degrees each

The sum of the measures of the four angles is 360 degrees, so we can write an equation:

20 + 20 + x + x = 360

Simplifying this equation, we get:

40 + 2x = 360

Subtracting 40 from both sides, we get:

2x = 320

Dividing both sides by 2, we get:

x = 160

Therefore, the measures of the other two angles in the parallelogram are both 160 degrees.

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