plzzz this lines and angles
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21
SOLUTION:-
∠MPN= ∠P - ∠QPN - ∠MPR
=)∠P - ∠QPN -1/2 ∠P
[Because MP is the angular bisector of ∠P]
=) 1/2 ∠P - ∠QPN
=) 1/2∠P- (90-∠Q)
[Because ∆PQN is right angled]
=) 1/2(180° - ∠Q -∠R)- (90°- ∠Q)
[Because sum of angles in ∆PQR is 180]
=) 90- ∠Q/2 - ∠R/2-90° + ∠Q
=) ∠Q/2 - ∠R/2
=) 1/2(∠Q- ∠R) [Proved]
Hope it helps ☺️
Answered by
2
SOLUTION:-
∠MPN= ∠P - ∠QPN - ∠MPR
=)∠P - ∠QPN -1/2 ∠P
[Because MP is the angular bisector of ∠P]
=) 1/2 ∠P - ∠QPN
=) 1/2∠P- (90-∠Q)
[Because ∆PQN is right angled]
=) 1/2(180° - ∠Q -∠R)- (90°- ∠Q)
[Because sum of angles in ∆PQR is 180]
=) 90- ∠Q/2 - ∠R/2-90° + ∠Q
=) ∠Q/2 - ∠R/2
=) 1/2(∠Q- ∠R) [Proved]
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