Answer :

Let us first construct diagram for the above proof:


QR is extended on both the sides.


In the figure, PQS and PRT are the two exterior angles.


It is given that PQR = PRQ which means that the given triangle is an isosceles triangle.


Hence length PQ = PR.


Now PQS + PQR = 180° ……(i) [as they form linear pair that angles in straight line always add up to 180°]


Similarly, PRQ + PRT = 180° ……. (ii).


For the equations (i) and (ii), the right-hand side is equal which means that the left-hand side should also be equal.


PQS + PQR = PRQ + PRT


PQS and PRQ gets eliminated as they both are equal angles.


So, we can state that PQS = PRT.


Hence it is proved that the measurement of external angles is equal.


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