Question

in the given fig angle Q>angle R and M is the midpoint on QR such that PM is the bisector of angle QPR. if the perpendicular from P on QR meets QR at N, prove that angle NPM=1/2(angle Q - angle R)

Answer 1

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Answer 2

Answer:

∠QPM=∠RPM

In ΔPNQ

∠QPN=90  

∘

−∠Q

In ΔPNR

∠RPN=90  

∘

−∠R

∠QPM=∠RPM

⇒∠QPN+∠MPN=∠RPN−∠MPN

⇒2∠MPN=∠RPN−∠QPN

⇒2∠MPN=(90  

∘

−∠R)−(90  

∘

−∠)

⇒∠MPN=  

2

1

​

(∠Q−∠R) (proved)

Step-by-step explanation: