In parallelogram ABCD, AC-diagonal, angle BCA = 20 °, angle BAC = 30 ° Find the angles of parallelogram ABCD.

1. Let us denote the angle by the symbol ∠.

2. We calculate the value of ∠B, taking into account that the total value of the angles of the triangle ABC is 180 °:

∠В = 180 ° – ∠АСВ – ∠ВАС = 180 ° – 20 ° – 30 ° = 130 °.

3. ∠ACB and ∠САD are equal as the angles formed by the parallel sides BC and A and the diagonal AC intersecting them:

∠АСВ = ∠САD = 20 °.

4.∠A = ∠BAC + ∠CAD = 30 ° + 20 ° = 50 °.

5. The angles of the parallelogram opposite each other are equal.

Therefore, ∠С = ∠А = 50 °, ∠В = ∠Д = 130 °.

Answer: ∠С = ∠А = 50 °, ∠В = ∠Д = 130 °.