Question

If the length of one side of a rhombus is equal to the length of its diagonals find the angles of the rhombus

Answer 1

Answer:

Construction-Draw a Rhombus ABCD. Draw diagonal AC.

In triangle ABC,

AB=BC=AC

Since Rhombus has all the sides equal and according to the question one of its diagonals is also equal.

Therefore ABC is an equilateral triangle

angle ACB=60°

angle BAC=60°

angle ACB=angle DAC (Alternate Interior Angles)

Angle BAC+Angle DAC= Angle BAD

60°+60°=Angle BAD

Angle BAD=120°

Angle BAD+Angle ADC=180° (Co-Interior Angles)

120°+ Angle ADC=180°

Angle ADC=60°

In a Rhombus, Opposite angles are equal

Angle BAD=Angle DCB

Angle ABC=Angle ADC

Therefore all angles are 120°,60°,120°,60°

Answer 2

Answer:

Step-by-step explanation:

Let ABCD is a rhombus

AB = BC = CD = DA

In triangle BAC

BA = BC = CA

therefore,

AngleBAC= angle ABC=angleACB= 60°.................(1)

log in triangle DAC, DA= DC= CA

angle DAC= angleACD= angle ADC= 60° ............(2)

from (1)&(2)

angle A= angleBAC+ angleDAC = 60°+60°=120°

angleB = angleABC=60°

angleC= angleACB+ angleACD= 60°+60°= 120°

angleA= angleADC=60°