Question

the measures of two adjacent angles of a parallelogram are in the ratio 2:3 find the meassures of each of the paralellogram
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Answer 1

Answer:

We know that opposite angles of a parallelogram are equal

We can write them as 2x,3x,2x,3x

So,

2x+2x+3x+3x=360° (we know sum of all angle of quadrilateral is 360°)

4x+6x=360°

10x=360°

x=360/10=36°

So

Measure of two opposite angles=3x=3*36=108°

Measure of other two opposite angles=2x=2*36=72°

I hope it will help you

Answer 2

Answer:

The angles P, Q, R, S are 72°, 108°, 72°, 108° respectively.

Step-by-step explanation:

Given:

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

To Find:

• The measure of each angle in the parallelogram

Solution:

Let the angles of the parallelogram be P, Q, R,S

Let Angle P = 2x

Let Angle Q = 3x

We know that in a parallelogram, adjacent angles are supplementary.

Hence,

Angle P + Angle Q = 180

2x + 3x = 180

5x = 180

x = 180/5

x = 36

Hence Angle P = 2x = 2 × 36 = 72°

Angle Q = 3x = 3 × 36 = 108°

Now we know that in a parallelogram opposite angles are equal.

Hence,

Angle R = Angle P = 72°

Angle S = Angle Q = 108°

Hence the angles P, Q, R, S are 72°, 108°, 72°, 108° respectively.

Verification:

In a quadrilateral sum of all angles = 360

Angle P + Angle Q + Angle R + Angle S = 360

72 + 108 + 72 + 108 = 360

180 + 180 =360

360 = 360

Hence verified.