Math, asked by ManickyaManickya, 1 year ago


plzzz this lines and angles​

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Answers

Answered by Anonymous
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 pv057966
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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