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 

$\angle$ QPO  =   $\angle$ SPO  =  $\frac{1}{2}$  $\angle$ QPS  ----------------- ( 1 )

And 

$\angle$ RSO  =   $\angle$ PSO  =  $\frac{1}{2}$  $\angle$ 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

$\angle$ QPS  +  $\angle$ RSP  =  180$°$

Divide by 2 on both hand , side , we get 

$\frac{1}{2}$  $\angle$ QPS  +    $\frac{1}{2}$  $\angle$ RSP =  90$°$  , So from equation 1 and 2 , we get

$\angle$ SPO  +  $\angle$ PSO  = 90$°$  -------------- (  3  )

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

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

90$°$  +  $\angle$ POS = 180$°$ 

So,

$\angle$ POS = 90$°$ 

Option  ( B  )  ( Ans )