Question

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

Answer 1

Given :

⬤ Two adjacent angles of a Parallelogram are in the Ratio 3 : 2 .

To Find :

⬤ Measure of Each Angle of Parallelogram .

Solution :

Let :

• Measure of First adjacent angle be 3x.
• Measure of Second adjacent angle be 2x.

As we know that , Sum of all adjacent angles of a Parallelogram is 180 degree . Hence ,

$\sf{3x+2x=180^{\circ}}$

5x = 180°

x = 180/5

x = 36°

Therefore , The Value of x is 36 degree .

Hence ,

Measure of First adjacent angle = 3x

= 3(36)

= 108°

Measure of Second adjacent angle = 2x

= 2(36)

= 72°

As Opposite angles of Parallelogram are equal . Therefore , Measure of Four adjacent angle are 108° , 72° , 108° and 72° .

Check :

3x + 2x = 180°

108 + 72 = 180°

180° = 180°

Hence Checked .