Question

If the bisectors of angles ∠PQR and ∠PRQ of triangle PQR meet at a point M, then prove that angle QMR = 90+1/2 angle p... please answer .......... please answer ......... please answer ......... please answer .........please answer .........please answer .........please answer .........please answer .........please answer .........

Answer 1

Given:

ΔPQR

Bisectors = ∠Q and ∠R

To Find:

∠QMR = 90 + ∠P/2,

Solution:

Bisectors of ∠Q and ∠R meet at point M.

Let ∠PQR =∠Q, ∠QRP =∠R and ∠QPR = 2P

In ΔPQR

∠P +∠Q+∠R = 180°  (sum of angles of a triangle)

= ( ∠Q +∠R = 180 − P ) --- eq 1

In ΔMQR

∠QMR + ∠Q/2 + ∠R/2 = 180°  (sum of angles of a triangle)

= (∠Q/2 + ∠R/2 = 180 - ∠QMR)

Thus, from equation 1 -

(180−∠P) /2  = 180 −∠QMR

90 - ∠P/2 = 180 −∠QMR

∠QMR = 90 + ∠P/2

Answer: ∠QMR = 90 + ∠P/2, hence proved