Question

pqrs is a square and poq is an equilateral triangle. what is the value of angle sor​

Answer 1

The value of SOR=$150^{\circ}$

Step-by-step explanation:

PQRS is a square

Angle P=Angle S=Angle Q=Angle R=90 degrees

POQ is an equilateral triangle

Angle POQ=Angle OQP=Angle OPQ=60 degrees

$\angle OQR=\angle Q-\angle PQO=90-60=30^{\circ}$

$\angle OPS=\angle P-\angle OPQ=90-60=30^{\circ}$

QO=QR

Angle QRO=Angle QOR

Reason: Angle made by two equal sides are equal

PO=PS

Angle POS=Angle PSO

In triangle ORQ

$\angle QRO+\angle QOR+\angle OQR=180$

Triangle angles sum property

Substitute the values then we get

$\angle QRO+\angle QRO+30=180$

$2\angle QRO=180-30=150$

$\angle QRO=\frac{150}{2}=75^{\circ}$

In triangle POS

$\angle POS+\angle PSO+\angle OPS=180$

Triangle angles sum property

Substitute the values then we get

$\angle POS+\angle PSO+30=180$

$2\angle POS=180-30=150$

$\angle POS=\frac{150}{2}=75^{\circ}$

Angle POQ+angle QOR+angle POS+angle SOR=360 degrees=Complete angle

Substitute the values then we get

$75+75+60+\angle SOR=360$

$\angle +210=360$

$\angle SOR=360-210=150^{\circ}$

#Learns more:

https://brainly.in/question/1146808;answered by brainly user