Find the angles of a parallelogram if they are 5: 1?

1. Vertices of the parallelogram – А, В, С, D. ∠В / ∠А = 5/1.

2.∠B = 5∠A.

2. To solve the problem, we will use one of the properties of the parallelogram: the total value of the angles located on one side (adjacent) is 180 °.

∠А + ∠В = 180 °.

3. Substitute in this expression 5∠A instead of ∠B:

∠А + 5∠А = 180 °.

6∠A = 180 °.

∠А = 180 °: 6 = 30 °.

∠B = 5∠A = 30 ° x 5 = 150 °.

4. Angles opposite each other (opposite) are equal:

∠А = ∠С = 30 °, ∠В = ∠Д = 150 °.

Answer: ∠А = ∠С = 30 °, ∠В = ∠Д = 150 °.