Question

one of the diagonals of a rectangle is equal to one of its sides.find the angles of the rhombus​

Answer 1

Lets consider, ABCD is rhombus of sides AB=BC=CD=DA=AC diagonal of rhombus.

In triangle ΔBAC,

BA=BC=CA

∠BAC=∠ABC=∠ACB=60

0

. . . . . . . (1)

In triangle ΔADC

DA=DC=CA

∠BAC=∠ACD=∠ADC=60

0

. . . . . . . .(2)

From equation (1) and equation (2), we get

∠A=∠BAC+∠ADC

∠A=60

+60

=120

∠B=∠ABC=60

∠C=∠ACB+∠ACD=60

+60

=120

∠D=∠ADC=60