If the adjacent angles of a parallelogram are equal, then the parallelogram is a
(a) rectangle
(b) trapezium
(c) rhombus
(d) any of the three

Solution:

Given, the adjacent angles of a parallelogram are equal.

We have to find the type of quadrilateral.

A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

We know that the sum of adjacent angles of a parallelogram are supplementary.

Given, both the angles are equal

So, each angle measures 90 degrees.

A rectangle is a closed two-dimensional figure with four sides.

The opposite sides of a rectangle are equal and parallel to each other.

All angles are equal to 90 degrees.

Therefore, the required parallelogram is a rectangle.

✦ Try This: The sum of adjacent angles of a parallelogram are (a) complementary, (b) supplementary, (c) right angles, (d) none of these

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 37

If the adjacent angles of a parallelogram are equal, then the parallelogram is a (a) rectangle (b) trapezium (c) rhombus (d) any of the three

Summary:

If the adjacent angles of a parallelogram are equal, then the parallelogram is a rectangle.

☛ Related Questions:

• Which of the following can be four interior angles of a quadrilateral? (a) 140°, 40°, 20°, 160° (b) . . . .
• The sum of angles of a concave quadrilateral is (a) more than 360° (b) less than 360° (c) equal to 3 . . . .
• Which of the following can never be the measure of exterior angle of a regular polygon? (a) 22° (b) . . . .