Q. 63.7( 3 Votes )

# Two straight line

Given: POT = 75°

Observe that ROP, POT, and TOS form a linear pair on line RS at point O.

ROP + POT + TOS = 180°

From the figure, we have ROP = 4b, POT = 75°, TOS = b

4b + 75° + b = 180°

5b + 75° = 180°

5b = 105°

Now, observe that QOS and ROP form a pair of vertically opposite angles.

QOS = ROP

From the figure, we have QOS = a, ROP = 4b

a = 4b

But, we found b = 21°

a = 4 × 21°

a = 84°

We also have ROQ and QOS forming a linear pair on line RS at point O.

ROQ + QOS = 180°

From the figure, we have ROQ = 2c, QOS = a

2c + a = 180°

But, we found a = 84°

2c + 84° = 180°

2c = 96°

Thus, a = 84°, b = 21° and c = 48°.

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