Question

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

Answer 1

If the adjacent angles of a parallelogram are equal. . .

firstly a parallelogram will have adjacent angles as supplementary. that means the angle will add up to 180 degrees.

If the adjacent angles are equal then we need to find

x + x = 180 => 2x = 180 => x = 90 degrees.

all the angles will be 90 degree.

hence it will be a rectangle.

Answer 2

$\bigstar$ Question:

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

$\bigstar$ Given:

• The adjacent angles of a parallelogram are equal.

$\bigstar$To find:

• What parallelogram is this?

$\bigstar$ Solution:

Let the adjacent angles be x.

So all the angles will be x.

(Since all are adjacent angles)

In a Quadrilateral, the sum of all angles is 360°.

$\therefore$ x + x + x + x = 360°

($\because$Sum of all angles in a Quadrilateral is 360°)

$\implies$ 4x = 360°

$\implies$ x = 360°/4

$\implies$x = 90°

$\therefore$ each angle is 90°.

When the opposite pair of sides are equal and parallel with one angle as 90°, then the Parallelogram is a rectangle.

$\bigstar$Answer:

• Therefore, if the adjacent angles in a parallelogram are equal, then it is a rectangle.