The two angles of the parallelogram are proportional to the numbers 5 and 13. Find the smaller angle of the parallelogram.

A parallelogram is a quadrilateral in which opposite sides are parallel and equal to each other, as well as opposite angles are equal. The sum of the angles of a parallelogram adjacent to one side of it is 180º. Since the degree measures of the angles of the parallelogram are proportional to the numbers 5 and 13, we express it this way:

∠А – 5x;

∠В – 13x;

5x + 13x = 180;

18x = 180;

x = 180/18 = 10;

∠А = 5 ∙ 10 = 50º;

∠В = 13 ∙ 10 = 130º.

Answer: The degree measure of the smaller parallelogram angle is 50º.