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In the diagram below of triangle KLM, N is a midpoint of KL and P is a midpoint of LM. If \(m\angle PNL = 2x + 61\) and \(m\angle MKN = 97 - 7x\), what is the measure of \(\angle PNL\)?

Answer :

The measure of angle PNL given that N is a midpoint of KL and P is a midpoint

of LM is 56.46°.

What is the measure of angle PNL?

N is a midpoint of KL and P is a midpoint of LM proves that triangle NLP is half the measure of triangle KLM.

So, NP is the corresponding side to KM.

Since KLM = 2 (NLP)

Then,

KM = 2 (NP)

KM = 97 - 7x

NP = 2x + 61

KM = 2 (NP)

97 - 7x = 2(2x + 61)

97 - 7x = 4x + 122

Combine like terms

97 - 122 = 4x + 7x

-25 = 11x

Divide both sides by 11

x = -25/11

= -2.27

Therefore,

angle PNL = 2x + 61

= 2(-2.27) + 61

= -4.51 + 61

= 56.46°

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