Choose the right answer

PQRS is a parallelogram. The angle bisector of angle P and angle S meet at O. The measure of angle POS is

A. 45

B. 90

C. 105

D. 60

Answer :



Here we know 

QPO  =   SPO  =  12  QPS  ----------------- ( 1 )

And 

RSO  =   PSO  =  12  RSP  ----------------- ( 2 )

From the properties of parallelogram , We know "  Adjacent sides (ones next to each other) of a parallelogram are supplementary.  This means that their measures add up to 180° .

So ,

Here

QPS  +  RSP  =  180°

Divide by 2 on both hand , side , we get 

12  QPS  +    12  RSP =  90°  , So from equation 1 and 2 , we get

SPO  +  PSO  = 90°  -------------- (  3  )

Now we know from angle sum property of triangle , So In triangle POS

  SPO  +  PSO  +  POS = 180°  , Substitute value from equation 3 , and get

90°  +  POS = 180° 

So,

POS = 90° 

Option  ( B  )  ( Ans )

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