Find the angles of the parallelogram ABCD, if it is known that angle A is 9 times greater than angle B

A parallelogram is a quadrangle in which opposite sides are parallel and equal, as well as opposite angles are equal:

∠А = ∠С;

∠В = ∠D.

The sum of the degree measures of the angles of the parallelogram adjacent to one side is 180º. Since the angle A is nine times the angle ∠B, we express it like this:

x – the degree measure of the angle ∠В and ∠D;

9x – the degree measure of the angle ∠A and ∠C;

x + 9x = 180;

10x = 180;

x = 180/10 = 18;

∠В = ∠D = 18º;

∠А = ∠С = 9 · 18º = 162º.

Answer: angles ∠А and ∠С are equal to 162º, angles ∠В and ∠D are equal to 18º.