Answer :

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


So in ΔPRS,


PQR+QRP+RPQ=180°


PQR+RPQ =180°-QRP………….(i)


Now QRS is a straight line, so


QRS=180°


QRS=QRP+PRS=180°


PRS=180°-QRP………(ii)


Substituting equation (ii) in equation (i), we get


PQR+RPQ=PRS


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


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