Question

A

3. In the diagram below, it is known that mNPQ = 9x - 25, mMPQ= 3x - 5, and mMPN = 4x+12. Using
this information, find the numerical value of mQPM.
​

Answer 1

m∠QPM=43°

Explanation:

see the attached figure to better understand the problem

we know that

m∠NPQ=m∠MPN+m∠MPQ

we have

m∠NPQ=(9x-25)°

m∠MPN=(4x+12)°

m∠MPQ=(3x-5)°

substitute the given values and solve for x

(9x-25)°=(4x+12)°+(3x-5)°

(9x-25)°=(7x+7)°

9x-7x=25+7

2x=32

x=16

Find the measure of angle QPM

Remember that

m∠QPM=m∠MPQ

m∠MPQ=(3x-5)°

substitute the value of x

m∠MPQ=(3(16)-5)=43°

therefore

m∠QPM=43°