Question

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Answer 1

GIVEN

PQR is a triangle PT is a bisector of angle P

QR is extended to S

R.T.P :- angle PQR + angle PRS = 2 * angle PTR

∡QPT =∡RPT [PT is a bisector of angle P]

∡PTR =∡PQR + ∡QPT

∡PQR = ∡ PTR - ∡QPT.......................[1]

∡ PRS =∡ PTR +∡ RPT....................[2]

ADDING [1] AND [2]

∡PQR+ ∡PQR = ∡ PTR - ∡QPT + ∡ PTR + ∡ RPT

∡PQR+ ∡ PQR = ∡ PTR - ∡ QPT + ∡ QPT + ∡PTR [ ∡QPT = ∡RPT]

∡ PQR+∡ PQR =∡ PTR +∡ PTR

∡PQR+ ∡ PQR = 2*∡ PTR PROVED