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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Answer:

60°, 120°

Step by Step Explanation:
  1. Following figure shows the rhombus ABCD,
  2. 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
  3. In ΔABC, AB = BC = CA,
    Hence, the ΔABC is a equilateral triangle.
  4. Similarly, the ΔACD is a equilateral triangle.
  5. All angles of a equilateral triangle is equal to 60°.
    Therefore, ∠B = ∠D = 60°,
    ∠A = ∠BAC + ∠CAD = 60° + 60° = 120°,
    Similarly, the ∠C = 120°
  6. Hence, the angles of the rhombus are 60° and 120°.

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