The diagonal of the parallelogram forms an angle of 20 degrees and 35 degrees with its two sides. Find a larger angle.

1. Vertices of the parallelogram – А, В, С, D. АС – diagonal. ∠CAD = 20 °. ∠АСD = 35 °.

2. We calculate the value of the degree measure ∠D:

∠САD + ∠АСD + ∠ADС (∠D) = 180 °.

∠D = 180 ° – ∠САD – ∠АСD = 180 ° – 20 ° – 35 ° = 125 °.

3. According to the property of the parallelogram, the total value of the degree measures of the angles located on one of its sides is 180 °:

∠D + ∠A = 180 °. ∠А = 180 ° – 125 ° = 55 °.

4. In a parallelogram, the angles opposite each other are equal:

∠А = ∠С = 55 °, ∠D = ∠В = 125 °.

Answer: The larger angle is 125 °.