Question

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
(a) 90°
(b) 120°
(c) 70°
(d) 80°

Answer 1

Hint: Recall that the adjacent angles of a parallelogram are supplementary and add up to 180°. It is given that the two adjacent angles are equal. Hence, equate them and find all the angles.

Complete step-by-step answer:
A quadrilateral is a closed polygon with four sides.

A parallelogram is a special type of quadrilateral that has opposite sides that are equal and parallel.

The opposite sides of a parallelogram are equal in length and the diagonals of the parallelogram bisect each other.

A rhombus, square, rectangle are all special kinds of a parallelogram.

Since the two pairs of opposite sides are parallel to each other, the opposite angles of a parallelogram are equal and the adjacent angles are supplementary.

Supplementary angles are two angles that add up to a sum of 180°.

In this problem, it is given that the adjacent angles of the parallelogram are equal.

Let the two adjacent angles of the parallelogram be equal to x and y. Since they are supplementary they add up to 180°.

\[x + y = 180^\circ ..........(1)\]

We are given that the adjacent angles are equal.

\[x = y.............(2)\]

Substituting equation (2) in equation (1), we have:

\[x + x = 180^\circ \]

\[2x = 180^\circ \]

\[x = 90^\circ \]

Hence, the value of all angles is 90°.

Hence, the option (a) is the correct answer.

Note: The adjacent angles are given to be equal, we know that the opposite angles are also equal, hence, all the angles are equal to each other. Hence, we can equate them to the sum of all angles of the quadrilateral, that is, 360° and solve for the value of the angles.