Question

The length of one of the diagonals of a rhombus is equal to the length of one of its sides. Find the angles of the rhombus.

Answer 1

Let ABCD be a rhombus such that the length of its diagonal BD is equal to the length of one of its sides.


That is, AB = BC = CD = AD = BD

$\therefore △$ABD is an equilateral triangle.

So, $\angle BAD={60}^{\circ }$

$\Rightarrow \angle BCD={60}^{\circ }$ [Opposite angles of a parallelogram are equal]

$\angle BAD+\angle ABC={180}^{\circ }$ [Adjacent angles of a parallelogram are supplementary]

$\Rightarrow \angle ABC={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$\angle ADC=\angle ABC={120}^{\circ }$ [Opposite angles of a parallelogram are equal]