Question

Hello !
PQRS is a rhombus. If ∠PSQ = 500, find the angles of the rhombus.

Answer 1

Given: PQRS is a rhombus

PQS= 50*

to find  - angle P,Q,R,S

i.e. PQS=PSQ(adjacent sides of a rhombus are equal)

in triangle PSQ

PSQ+PSQ+P=180*

2PSQ+P=180*

100+P=180*

P=80*

also ,P=R=80*

angle P+Q=180*(when two lines are parallel and cut by a transversal then  angles formed are supplementary)

so angle Q= 180- P

            Q=180-80=100*

 also     Q=S=100*

So , Angle P and R= 80*

and    Q and S = 100*

Thank.................................

Answer 2

m PQS= 50*

PQS=PSQ

PSQ is forming a triangle,

a+b+c = 180*

PSQ + PSQ + P = 180*

2(PSQ)+P = 180*

2(50)+P = 180*

P = 180 - 100

= 80*

P = R = 80

Q = 180 - P

= 180 - 80

= 100*

Q = S = 100*