Answer :

The given figure is as shown below:



Given PRQ = 60°, QPR = 50°, QST = 30°


To find the exterior angle, i.e., ext STR = x°


Now consider ΔPQR


We know in a triangle the sum of all three interior angles is equal to 180°.


So in this case,


PRQ + PQR + QPR = 180°.


Substituting the values, we get


60° + PQR + 50° = 180°


PQR = 180° - 60° - 50°


PQR = 70°


Now PQS is a straight line, so


PQS = 180°


PQR + SQT = 180°


Now substituting the values, we get


70° + SQT = 180°


SQT = 180° - 70°


SQT = 110°


From figure consider ΔQST, so


In this triangle STR is exterior angle,


And we know the measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.


Hence STR = QST + SQT


Substituting the values, we get


⇒∠STR = 30° + 110°


⇒∠STR = 140°


So the measurement of exterior angle in the given figure is 140°.


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