Q. 63.7( 3 Votes )

Two straight line

Answer :

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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