Question

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

Answer 1

One of the diagonals of a rhombus is equal to one of its sides.

We know that a rhombus has four equal sides. If one side has the same length as a diagonal, the diagonal is part of two equilateral triangles.Since a rhombus has four sides we can say
AB =BC=CD = DA..............(a)

Rhombus = ABCD
where AB = diagonal of AC
from (a)
AB = BC = AC
Since the triangle, ABC is equilateral and so angle ABC = 60. To solve the problem we can make an equation.
now from figure 2
let angle DAB = x

60 + x = 180 [co - interior angle]


Solve

60 + x = 180
180 - 60 = x
x = 120

angle DAB = angle DCB = 120 [opposite of prallalogram angle]
angle ABC =angleADC = 60 [opposite of prallalogram angle]