Mathematics
One of the diagonals of a rhombus and its sides are equal. Find the angles of the rhombus.
Quadrilaterals
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Answer
One of the diagonals of a rhombus and its sides are equal.
ABCD is the rhombus and AC is the diagonal such that AC = AB.
In triangle ABC,
AB = BC (Sides of rhombus)
AB = AC (Given)
⇒ AB = AC = BC
So, triangle ABC is a equilateral triangle.
Therefore, ∠ B = 60°, ∠ BAC = 60° and ∠ BCA = 60°.
Similarly, triangle ADC is a equilateral triangle.
Therefore, ∠ D = 60°, ∠ DAC = 60° and ∠ DCA = 60°
∠ A = ∠ BAC + ∠ DAC
= 60° + 60°
= 120°
∠ C = ∠ BCA + ∠ DCA
= 60° + 60°
= 120°
Hence, the value of ∠ A = 120°, ∠ B = 60°, ∠ C = 120° and ∠ D = 60°.
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