Find the angles of parallelogram ABCD if you know that angle B is 50 degrees greater than angle A.

1. According to the condition of the problem, ∠В is more than the angle ∠А by 50 °:

∠В – ∠А = 50 °.

2. ∠В + ∠А = 180 ° (according to the properties of the parallelogram).

3. Add these expressions:

∠В – ∠А + ∠В + ∠А = 230 °.

2∠B = 230 °.

∠В = 115 °.

∠А = 180 ° – ∠В = 180 ° – 115 ° = 65 ° or ∠А = ∠В – 50 ° = 115 – 50 ° = 65 °.

4.∠А = ∠С = 65 °. ∠В = ∠D = 115 ° (in a parallelogram the angles opposite each other are equal).

Answer: the angles of the parallelogram ABCD are ∠A = ∠C = 65 °, ∠B = ∠D = 115 °.