The angles formed by the diagonals of a rhombus on one of its sides are 1: 4. Find the corners of the diamond.

1. Vertices of the rhombus A, B, C, D. AC and BD are diagonals. O is the point of their intersection.

∠DAO / ∠ADO = 1/4.

2. By the condition of the problem ∠DAO / ∠ADO = 1/4. Consequently, ∠ADO = 4∠DAO.

3. ∠DAO + ∠ADO + ∠АОD = 180 °. ∠АD = 90 °, since the diagonals of the rhombus are perpendicular.

4. Substitute in this expression 4∠DAO instead of ∠ADO:

∠DAO + 4∠DAO + 90 ° = 180 °.

5∠DAO = 90 °.

∠DAO = 18 °.

∠ADO = 18 x 4 = 72 °.

5. Since the diagonals of the rhombus are bisectors, and the opposite angles are equal:

∠А = ∠С = 18 ° x 2 = 36 °, ∠D = ∠В = 72 ° x 2 = 144 °.