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

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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

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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°.