Question

Two adjacent angles of a paralle

logram are congruent. What is the measure of
each?

​

Answer 1

`90^(\circ)`. In other words, these two angles are both right angles, and this parallelogram would be a rectangle.

Explanation:

Two angles that congruent have the same size.

At the same time, those two adjacent angles of this parallelogram would be a pair of consecutive interior angles. Because the two sides of a parallelogram are parallel to one another, the sum of these two consecutive interior angles would be
`180^(\circ)`- they are supplementary to one another.

Let the two angles be
`\angle1` and
`\angle 2`.

`\angle 1 = \angle 2` because the two angles are congruent.

`\angle 1 + \angle 2 = 180^(\circ)` because these two angles are adjacent angles of a parallelogram.

Hence,
`\displaystyle \angle 1 = \angle 2 = (1)/(2) * 180{^\circ} = 90^(\circ)`.