Question

In the given figure.,the bisectors of angle P and angle Q meet at a point O. If angle R =100 degree and angle S=50 degree,find angle POQ​

Answer 1

Answer:

POQ=40 Degree

Step-by-step explanation:

First by using law opposite sides are equal and opposite angles are equal

S=50° , p=50°

At the same time Q=100°

It is a equalatral triangle

So, the outer angle are minus by inner angle

:. POQ= S-10°

=50°-10°

=40°

Answer 2

Step-by-step explanation:

We know that sum of interior angles of quadrilateral is 360

o

∠P+∠Q+∠R+∠S=360

o

∠P+∠Q+100+50=360

∠P+∠Q=210

o

……………..(1)

OP and OQ are bisectors of angles P and Q,

∠P=2∠OPQ and ∠Q=2∠OQP

So from (i), we have

2∠OPQ+2∠OQP=210

o

2(∠OPQ+∠OQP)=210

o

∠OPQ+∠OQP=105

o

…………….(2)

Consider triangle POQ,

∠POQ+∠OPQ+∠OQP=180

o

∠POQ+105

o

=180

o

[using equation (3)]

∠POQ=180

o

−105

o

∠POQ=75

o

.