In a parallelogram ABCD, if ∠ A=(3x-20)°, ∠ B = (y+15)° and ∠ C = (x+40)°, then find the values of x and y.

Question

In a parallelogram ABCD, if &#x2220; A=(3x-20)&#xB0;, &#x2220; B = (y+15)&#xB0; and &#x2220; C = (x+40)&#xB0;, then find the values of x and y.

Philoid · Accepted Answer

Given,

In parallelogram ABCD

Opposite Angles are equal.

∴ ∠ A = ∠ C

⇒ 3x-20 = x + 40

⇒ 2x = 60

⇒ x = 30

Consecutive angles are supplementary (A + B = 180°).

⇒ 3x – 20 + y + 15 = 180

⇒ 3x + y = 185

⇒ 3 × 30 + y = 185

⇒ y = 185 – 90 = 95