Question

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

Answer 1

ANSWER :-

We know that ,

Opposite Sides of parallelogram are parallel...

So, the adjecent angle will be interior angles of the transversal....which has the sum 180°.

So, let 3x and 2x be the angles....

➜ 3x + 2x = 180°

➜ 5x = 180°

➜ x = 36°

So, the angles are ...

3x = 36 × 3 = 108°

2x = 2 × 36 = 72°

Now ,

We know ,

opposite angles of parallelegram are equal...

So, the angles of parallelogram are 108°,72°,108°,72°.

Answer 2

Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.

Since the adjacent angles of a parallelogram are supplementary.

∠A+∠B=180⁰

⇒3x+2x=180 ⁰

⇒5x=180 ⁰

⇒x= $\frac{180⁰}{5}$

=36 ⁰

∴∠3×36⁰

=108⁰

and, ∠B=2×36⁰

=72 ⁰

Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108⁰

and ∠D=∠B=72⁰

Hence, ∠A=108⁰

,∠B=72 ⁰

,∠C=108 ⁰

and ∠D=72⁰