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 $110°$
• B. $60°$ and $120°$
• C. $80°$ and $100°$
• D. $120°$ and $240°$

Answer 1

The correct option is B $60°$ 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, $\angle ABD=\angle BDA=\angle BAD=60°$
Also, in triangle BCD, we get,
$\angle BCD=\angle CDB=\angle CBD=60°$
We know that opposite angles of a rhombus are equal.
So, we have,

Thus, we get,
$\angle A=\angle C=60°$
$\angle B=\angle D=60°+60°=120°$
So, the distinct angles of the rhombus are $60°$ and $120°$.

So, the correct answer is option (b).