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
POT = 75
So,
POR + POT + TOS = 180 ( Linear pair angles )
Now substitute given values , we get
4b + 75 + b = 180
5b + 75 = 180
5b = 105
b = 21
And
POR = 4b = 4 ( 21 ) = 84
And
SOQ = POR ( Vertically opposite angles )
Substitute values , we get
a = 84
And
QOR = POS ( Vertically opposite angles )
Substitute values , we get
2c = 75 + 21
2c = 96
c = 48
So,
a = 84 , b = 21 and c = 48 ( Ans )
We have two straight lines PQ and RS .
And
POT = 75
So,
POR + POT + TOS = 180 ( Linear pair angles )
Now substitute given values , we get
4b + 75 + b = 180
5b + 75 = 180
5b = 105
b = 21
And
POR = 4b = 4 ( 21 ) = 84
And
SOQ = POR ( Vertically opposite angles )
Substitute values , we get
a = 84
And
QOR = POS ( Vertically opposite angles )
Substitute values , we get
2c = 75 + 21
2c = 96
c = 48
So,
a = 84 , b = 21 and c = 48 ( Ans )