Question

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

Answer 1

Solutions 

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 

Rhombus = ABCD where AB = diagonal of AC 
Since the triangle ABC is equilateral and so angle ABC = 60. To solve the problem we can make an equation. 

60 + x = 180 

Solve 

60 + x = 180 
180 - 60 = x 
x = 120 

Answer = 120 

Answer 2

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

diagonal divide the Rhombus into two equal parts so it form equilateral triangle

all the angle be 60 °
angle BAC = Angle ABC = angle BCA = 60°

Angle B = Angle B = 60°
angle Dequal to 60°
Angle B equal to 60°

let angle A and angle C be x
Angle B + angle D + angle A + angle C = 360°

60 ° + 60°+ x + x = 360°
2 x = 360 - 120
2x = 240
x = 120
angleA = 120°
Angle B= 60°
anglesC= 120°
angle D= 60°

I hope it helps
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