Question

2. A rhombus is such that one of its diagonals is equal
to the side of the rhombus. Find the angles of the
rhombus.​

Answer 1

Let ABCD is a rhombus in which AB=BC=CD=DA=diagonal CA.

In triangle BAC

BA=BC=CA , therefore

angle BAC=angle ABC= angle ACB =60°………(1)

Similarly in triangle DAC , DA=DC=CA , therefore

Angle DAC=angle ACD=angle ADC=60°……….(2)

From eqn. (1) and (2)

Angle A=angle BAC+angle DAC=60°+60°=120°

Angle B= angle ABC = 60°.

Angle C=angle ACB+angle ACD=60°+60°=120°

Angle D =angle ADC=60°.