Question

the measure of two adjacent of a parallelogram are in the ratio 3:2 find the measure of each of the angels of the parallelogram

Answer 1

Correct Question :

The measure of two adjacent angles of a parallelogram are in the ratio 3:2 find the measure of each of the angels of the parallelogram

Answer :

the angles of the parallelogram are 72° , 108° , 72° and 108°

Step-by-step explanation :

Given :

the measure of two adjacent angles of a parallelogram are in the ratio 3:2

To find :

the measure of each angle.

Solution :

Let the adjacent angles be

• 3x
• 2x

In a parallelogram, the adjacent angles are supplementary angles.

i.e., The sum of the measures of the adjacent angles = 180°

➙ 3x + 2x = 180°

➙ 5x = 180°

➙ x = 180°/5

➙ x = 36°

⇒ 2x = 2 × 36° = 72°

⇒ 3x = 3 × 36° = 108°

The adjacent angles of the parallelogram are 72° and 108°.

Also, in a parallelogram the measure of the opposite angles are equal.

Hence, the angles of the parallelogram are 72° , 108° , 72° and 108°