Question

One of the diagonals of a rhombus is equal to its one side. Find all the angles of the rhombus.

Answer 1

Diagonal of rhombus is equal to side of rhombus (given)

Diagonal divides the Rhombus into two equal parts so it forms an equilateral triangle

All the angle be ${60}^{\circ }$ and $\angle BAC=\angle ABC=\angle BCA={60}^{\circ }$

$\angle B=\angle D={60}^{\circ }$

Let $\angle A$ and $\angle C$ be $x$

$\angle B+\angle D+\angle A+\angle C={360}^{\circ }$

$\Rightarrow {60}^{\circ }+{60}^{\circ }+x+x={360}^{\circ }$

$\Rightarrow 2x=360-120$

$\Rightarrow 2x=240$

$\therefore x={120}^{\circ }$

$\therefore \angle A={120}^{\circ }$,$\angle B={60}^{\circ }$,$\angle C={120}^{\circ }$,$\angle D={120}^{\circ }$