Question

Two adjacent angles of a paralle
logram are congruent. What is the measure of
each?

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Answer 1

Answer:

$90^{\circ}$. In other words, these two angles are both right angles, and this parallelogram would be a rectangle.

Step-by-step 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, $\displaystyle \angle 1 = \angle 2 = \frac{1}{2} \times 180{^\circ} = 90^{\circ}$.