Find the angles of a parallelogram if an obtuse angle is known to refer to an acute angle as 8: 1.

1. Vertices of the parallelogram – A, B, C, D. ∠B: ∠A = 8: 1.

2. ∠В: ∠А = 8: 1 according to the problem statement. Therefore, ∠B = 8∠A.

3. The total value of the angles of the parallelogram located on one side (adjacent to it) is 180 °.

∠А + ∠В = 180 °. We replace ∠В with 8∠А in this expression:

∠А + 8∠А = 180 °.

9∠A = 180 °.

∠А = 20 °.

∠В = 8∠А = 8 x 20 = 160 °.

4. The angles of the parallelogram opposite each other are equal:

∠А = ∠С = 20 °. ∠В = ∠D = 160 °.

Answer: ∠А = ∠С = 20 °. ∠В = ∠D = 160 °.