In Fig. two straight lines PQ and RS intersect each other at O. If angle POT = 75°,find the values of a,b and c.

Answer :

We have two straight lines PQ and RS .
And
$\angle$ POT  =  75$°$

So,
$\angle$ POR  +  $\angle$ POT  +  $\angle$ TOS =  180$°$                        (  Linear pair angles )

Now substitute given values , we get

4b  + 75$°$  + b  =  180$°$

5b  +  75$°$  =  180$°$

5b  =  105$°$

b  =  21$°$ 
And
$\angle$ POR =  4b  =   4  (  21 )   =  84$°$  
And
$\angle$ SOQ = $\angle$ POR                                (  Vertically opposite angles ) 
Substitute values , we get

a = 84$°$  
And
$\angle$ QOR = $\angle$ POS                                (  Vertically opposite angles ) 
Substitute values , we get

2c = 75 $°$  +  21$°$  

2c  = 96$°$

c  =  48$°$  

So,

a  = 84$°$  ,   b  =  21$°$  and c  =  48$°$                                            ( Ans )