Question

VERIFY THAT THE EXTERIOR ANGLE IS EQUAL TO SUM OF INTERIOR OPPOSITE ANGLE

Answer 1

Because an exterior angle is equal to the sum of the opposite interior angles, it follows that it must be larger than either one of them.An exterior angle of a triangle is always larger then either opposite interior angle.

Answer 2

Given: let angle PRS be an exterior angle of triangle PQR.

we have to prove that:angle PRS is equal to sum of angles PQR and QPR

(note:I am writing angle as this symbol )

verification : The sum of all angles of a triangle is 180 degree.

Therefore,PQR+QPR+PRQ=180 degree __(1)

PRQ+PRS=180 degree (linear pair)__(2)

From (1) & (2)

PQR+QPR+PRQ = PRQ+PRS

Therefore

PQR+QPR = PRS (Reason:eliminating PRQ from both sides)

(refer to the attach diagram then you will understand)

Hence, It is verified that THE EXTERIOR ANGLE IS EQUAL TO SUM OF INTERIOR OPPOSITE ANGLE

HOPE YOU HAVE UNDERSTOOD MATE...

Please follow