Question

In the parallelogram ABCD, ∆A: ∆B=3:2. Let us write the measures of the angles
of the parallelogram​

Answer 1

Answer:

Given,

∠A : ∠B = 3 : 2

Let ∠A = 3x

and ∠B = 2x

We know, In a parallelogram sum of adjacent angles is 180°

⇒ ∠A + ∠B = 180°

⇒ 3x + 2x = 180°

⇒ 5x = 180°

⇒ x = 36°

Now, ∠A = 3(36) = 108°

∠B = 2(36) = 72°

Also, Opposite angles of a parallelogram are equal

⇒ ∠A = ∠C = 108°

⇒ ∠B = ∠D = 72°

Step-by-step explanation:

Answer 2

Corrected Question :

• In the parallelogram ABCD, ∠A: ∠B=3:2. Let us write the measures of the angles of the parallelogram.

Given :

• ABCD is a parallelogram

• Ratio of the angles ∠A: ∠B=3:2

To find :

• Measure of the angles of parallelogram

Solution :

A parallelogram ABCD is given.

Here,

∠A: ∠B=3:2

Let measure of angle A be 3x and measure of angle B be 2x.

∠A and ∠B are adjacent angles of the parallelogram.

We know that the sum of the adjacent angles is 180 degrees.

→ ∠A + ∠B = 180°

→ 3x + 2x = 180°

→ 5x = 180°

→ x = 180°/5

→ x = 36°

→ The value of x = 36°

Now,

→ ∠A = 3x

→ ∠A = 3 × 36°

→ ∠A = 108°

→ ∠B = 2x

→ ∠B = 2 × 36°

→ ∠B = 72°

Also we know that the opposite angles of a parallelogram are equal.

→ ∠A = ∠C = 108°

→ ∠B = ∠D = 72°

Therefore the measures of the angles of the parallelogram are 108°, 72°, 108° and 72°.

Pictorial representation in attachment.