Question

in triangle given below prove that

Answer 1

angle PQR = angle PTR - angle QPT -----(i)

angle PRS = angle QPR + angle PQR ----(ii)

Adding (i) and (ii)

angle PQR + angle PRS = angle PTR - angle QPT + angle QPR + angle PQR

angle PQR + angle PRS = angle PTR - angle QPT + 2angle QPT + angle PQR ( since angle QPR = angle QPT and angle QPR = angle QPT + angle QPR which equals 2angle QPT)

angle PQR + angle PRS = angle PTR + angle QPR + angle PQR

angle PQR + angle PRS = angle PTR + angle PTR

( since angle PTR is exterior angle of ∆QPT , •°• it equals to sum of two opposite interior angles , in this case , it equals angle QPT + angle PQR , also angle QPT = angle QPR , said above)

•°• angle PQR + angle PRS = 2 angle PTR

Hence , Proved