Question

in a parallelogram ABCD angle ACD equal to 50 degree and angle ADC is equal to 60 degree find the magnitude of angle ABC and ACB please answer​

Answer 1

Answer:

In a parallelogram ABCD, ∠A =x°, ∠B = 3x +20°, find x and find ∠C and ∠D.

ANSWER:

In parallelogram ABCD, ∠A and ∠B are adjacent angles supplementary to each other.



Thus, we have:

∠A + ∠B = 180°

Also,

∠A = x° and ∠B = (3x + 20)°

⇒ x° + 3x° + 20° = 180°

⇒ 4x° + 20° = 180°

⇒ 4x° = 160°

⇒ x° = 40°

⇒ x = 40

We know that opposite angles of a parallelogram are congruent.

Thus, we have:

∠C = ∠A = x°

⇒∠C= 40°

∠D = ∠B

⇒  ∠D     = 3x° + 20°

                 = 3(40°) + 20°

                 = 120° + 20°

                 = 140°

∴∠D=140°