The diagonal AC of parallelogram ABCD makes angles of 45 and 25 with its sides.

The diagonal AC of parallelogram ABCD makes angles of 45 and 25 with its sides. Find the angle larger than the angle of the parallelogram.

The diagonal AC of the parallelogram ABCD divides it into two equal triangles ABC and ADC, in each of them two angles are formed by this diagonal and the sides of the parallelogram. Since the sum of these angles is 45 ° + 25 ° = 70 °, then the large angles of the parallelogram are angles B and D, which are equal to each other. Knowing that the sum of the angles of any triangle is 180 °, it turns out: in triangles ABC and ADC, angle B = angle D = 180 ° – (45 ° + 25 °) = 110 °.
Answer: The degree measure of the large angles B and D of the parallelogram ABCD is 110 °.