In a rhombus, one of the diagonals is equal to a side of the rhombus. Find the angles of the rhombus.
Answer:
60°, 120°
- Following figure shows the rhombus ABCD,
- We know that, all sides of a rhombus have equal length.
According to the question, the diagonal AC of the rhombus ABCD is equal to the side of the rhombus.
Therefore, AB = BC = CD = DA = AC - In ΔABC, AB = BC = CA,
Hence, the ΔABC is a equilateral triangle. - Similarly, the ΔACD is a equilateral triangle.
- All angles of a equilateral triangle is equal to 60°.
Therefore, ∠B = ∠D = 60°,
∠A = ∠BAC + ∠CAD = 60° + 60° = 120°,
Similarly, the ∠C = 120° - Hence, the angles of the rhombus are 60° and 120°.
