Question

1. In parallelogram ABCD, ZA = 3 times ZB.
Find all the angles of the parallelogram. In the
same parallelogram, if AB = 5x - 7 and
CD = 3x + 1; find the length of CD.​

Answer 1

Answer:

Let ∠B = x.

Then, ∠A = 3x.

We know that opposite sides of a parallelogram are equal.

⇒ ∠A = ∠C = 3x

⇒ ∠B = ∠D = x.

We know that Sum of the parallelogram angles is equal to 360°.

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 3x + x + 3x + x = 360°

⇒ 8x = 360°

⇒ x = 45°.

Then,

⇒ 3x = 3(45) = 135.

Hence, the angles are : 135°,45°,135°,45°.

Now,

Given that AB = 5x - 7 and CD = 3x + 1

We know that opposite sides of a parallelogram are equal.

⇒ AB = CD

⇒ 5x - 7 = 3x + 1

⇒ 2x = 8

⇒ x = 4.

Substitute x in CD, we get

⇒ 3x + 1

⇒ 3(4) + 1

⇒ 13.

Therefore, the length of CD = 13.