Question

lines and angles { In the given figure, two straight lines PQ and RS intersect each other at O. If ∠POT = 75°, find the values of a, b, c.}

Answer 1

I have attached a rough sketch with this question. Hopefully this sketch is correct.

$\bold\pink{\fbox{\sf{Solution}}}$

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°