Diagonals of a Rhombus Bisect Each-Other at Right Angles
One of the di...
Question
One of the diagonals of a rhombus is equal to a side of the rhombus. The distinct angles of the rhombus are
A
70° and 110°
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B
60° and 120°
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C
80° and 100°
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D
120° and 240°
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Solution
The correct option is B60° and 120° In a rhombus all sides are equal.
It is given that a diagonal is equal to the side of a rhombus.
Thus, we have,
So, AB=BC=CD=AD=BD
That is, triangle ABD is an equilateral triangle as all the sides are equal.
So, ∠ABD=∠BDA=∠BAD=60°
Also, in triangle BCD, we get, ∠BCD=∠CDB=∠CBD=60°
We know that opposite angles of a rhombus are equal.
So, we have,
Thus, we get, ∠A=∠C=60° ∠B=∠D=60°+60°=120°
So, the distinct angles of the rhombus are 60° and 120°.