In a rhombus, one of the diagonals is equal to a side of the rhombus. Find the angles of the rhombus.
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Step by Step Explanation:
- 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°.