Question

If 2 straight lines PQ and RS intersect each other at O, if angle POT=75 0 Find the values of a, b and c

Answer 1

I have attached a rough sketch with this question. Hopefully this sketch is correct.
Solution:-
We have two straight lines PQ and RS. 
And,
∠ POT = 75°
So,
∠ POR + ∠ POT + ∠ TOS = 180° (Linear pair angles)
Now substitute the given values, we get
4b + 75° + b = 180°
5b = 75° = 180°
5b = 180° - 75°
5b = 105°
b = 21°
And, ∠ POR = 4b = 4 (21)
∠ POR = 84°
And,
∠ SOQ = ∠ POR   (vertically opposite angles)
Substitute the values, we get
a = 84°
And,
∠ QOR = ∠ POS (vertically opposite angles)
Substitute the values, we get
2c = 75° + 21°
2c = 96°
c = 96/2
c = 48°
So,
a = 84°
b = 21°
c = 48°

 

Answer 2

answer of this question is in figure