The degree measures of the two angles of a parallelogram are 4: 5. Find all the angles of the parallelogram.

1. Vertices of the parallelogram – A, B, C, D.

2. ∠А: ∠В = 4: 5. А = 4∠В / 5.

3. According to the property of the parallelogram, the total value of the degree measures of the angles located on one of its sides (adjacent to it) is 180 °:

∠А + ∠В = 180 °.

4. Replace этомA in this expression with 4∠B / 5:

4∠В / 5 + ∠В = 180 °.

9∠B / 5 = 180 °.

∠В = 5 x 180 ° / 9 = 100 °.

∠А = 4 x 100 ° / 5 = 80 °.

5. In a parallelogram, the angles opposite each other are equal:

∠А = ∠С = 80 °, ∠В = ∠D = 100 °.

Answer: ∠А = ∠С = 80 °, ∠В = ∠D = 100 °.