The diagonal of the parallelogram makes angles of 25 ° and 35 ° with the sides. Find the angles of a parallelogram?

univerkov | March 1, 2021 | education

1. Vertices of the parallelogram – A, B, C, D. AC – diagonal. ∠CAD = 25 °. ∠АСD = 35 °.

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

∠D = 180 ° – (∠САD + ∠АСD) = 180 ° – (25 ° + 35) ° = 120 °.

3. ∠D and ∠A – adjacent to the AC side. Therefore, the total value of their degree measures is 180 ° (according to the properties of the parallelogram):

∠D + ∠A = 180 °. ∠А = 180 ° – 120 ° = 60 °.

4. In a parallelogram the angles opposite each other are equal: ∠А = ∠С = 60 °, ∠D = ∠В = 120 °.

Answer: ∠А = ∠С = 60 °, ∠D = ∠В = 120 °.

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