Find angle D in parallelogram ABCD if one of the angles is 30 ° greater than the other.

A parallelogram is a quadrangle in which opposite sides are parallel and equal to each other.

The sum of the angles of a parallelogram adjacent to one side is 180º. Since the angle ∠A of the parallelogram is 30º greater than the angle ∠B, then we express:

x is the degree measure of the angle ∠В;

x + 30 – degree measure of angle ∠A;

x + x + 30 = 180;

x + x = 180 – 30;

2x = 150;

x = 150/2 = 75;

∠В = 75º;

∠А = 75º + 30º = 105º.

Answer: the angle ∠А is equal to 105º, the angle ∠В is equal to 75º.