A

Mathematics

1 answer:

tester [12.3K]9 days ago

7 0

The measure of angle QPM is 43°

Step-by-step explanation:

Refer to the attached illustration for better clarity regarding the problem. We know that the measure of angle NPQ can be expressed as the sum of angles MPN and MPQ:

m∠NPQ = m∠MPN + m∠MPQ

We have the values: m∠NPQ = (9x-25)°, m∠MPN = (4x+12)°, and m∠MPQ = (3x-5)°. When substituting the supplied values, solve for x using the equation (9x-25)° = (4x+12)° + (3x-5)°. This simplifies to (9x-25)° = (7x+7)°. Following through, the equation becomes 2x = 32, so x = 16. Now, we compute the measure of angle QPM, recalling that m∠QPM equals m∠MPQ, which gives us m∠MPQ = (3x-5)°. Plugging in the value of x leads to m∠MPQ = (3(16)-5) = 43°. Thus, m∠QPM is confirmed to be 43°

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