The diagonal of one side of a rhombus are of equal length. Find the measure of angles of the rhombus.

Consider ABCD is a rhombus

We know that

All sides are equal in rhombus

=> AB=BC=CD=DA

and AC and BD are digonals

Given that

Diagonal and the side of the rhombus are equal.

=> AB = BC = CD = DA = AC

Diagonal AC divides the rhombus into two triangles .

They are ∆ BAC and ∆ DAC

In triangle BAC

BA=BC=AC,(Given)

=> < BAC=<ABC= < ACB =60°………(1)

Similarly in ∆DAC ,

DA=DC=AC

=><DAC=<ACD=<ADC=60°……….(2)

From (1) and (2)

<A=<BAC+< DAC=60°+60°=120°

and

< B= < ABC = 60°.

and

<C=<ACB+<ACD=60°+60°=120°

and

< D =<ADC=60°

Therefore, <A = 120° , <B = 60° ,<C = 120° ,<D = 60°

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The measures of the all angles in the rhombus are 120° , 60° ,120° and 60°

Used formulae:-

all sides in a rhombus are equal