The diagonal of the parallelogram makes angles of 20 and 50 with the sides. Find the larger angle of the parallelogram.

By the condition of the problem, a parallelogram is given.

It is known that the degree measures of two angles, which are formed with the sides and the diagonal of a given parallelogram, are equal to 20 ° and 50 °, respectively.

Let’s determine how many degrees one of the angles of the parallelogram is:

20 + 50 = 70 °.

Let’s calculate how many degrees the second angle is, taking into account that the degree measure of all angles of the parallelogram is 360 °.

(360 – 70 * 2) / 2 = (360 – 140) / 2 = 220/2 = 110 °.

Answer: The larger angle in the parallelogram is 110 °.