Question

the sum of two adjecent angles of a parallelogram are in the ratio 3:2. find the measure of each of the angles of the parallelogram?

Answer 1

Let one adjacent ∠ be 3x°

So, the other adjacent ∠ be 2x°

According to Question,

Sum of adjacent ∠s of ||gm = 180°

3x + 2x = 180

⇒ 5x = 180

⇒ x = 180 / 5

⇒ x = 36

Required angles »

3x° = 3(36)° = 108°

2x° = 2(36)° = 72°

Hence, the required adjacent angles of the parallelogram are 108° & 72°.

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Answer 2

Given :

Ratio of 2 adjacent angles of a parallelogram = 3:2

To Find : Measure of each angles.

Solution :

Let the angles' ratio in the form of x :

3x , 2 x , 3x , 2x (Opposite angles in a parallelogram are equal)

Now ,

3x+2x+3x+2x =360°

10x = 360°

x= 360°/10 = 36°

3x = 3(36°) = 108°

2x = 2(36°) = 72°

Hence the required angles = 108°, 72°, 108° , 72° .

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