Question

PQRS is a rhombus and PRS=45degree. Find PQR .​

Answer 1

Answer:

Given that PQRS is a rhombus

∠PSR=∠PQR=54

∘

(opp. ∠S of a rhombus are equal)

⇒∠OSR=

2

1

×∠PSR=

2

1

×54

∘

=27

∘

(SQ bisects ∠PSR)

Now in ΔOSR

∠ORS+∠ROS+∠OSR=180

∘

⇒∠ORS+27

∘

+90

∘

=180

∘

(Diagonals of a rhombus bisect each other at right ∠s)

⇒∠ORS=63

∘

⇒∠PRS=63

∘