Question

A diagonal and a side of a rhombus are of equal length. Find the measure of the angles of the rhombus?

Answer 1

In triangle PQR
angle QPR+anglePRQ+anglePQR=180°
(sum of measure of all angle of a triangle is 180°)
=x+x+x=180°
=3x=180°
=x=60°
QPR=PRQ=PQR=60°
in rhombus opposite angle are congruent
PQR=PSR=60°
adjacent angle of rhombus are supplementary
SRQ=180-60
SRQ=120°
SRQ=SPQ(opposite angle of a rhombus are congruent)