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which are the correct measures for <klm, <kln, and <nml?
select one:
a. <klm = 63°, <kln = 24°, and <nml = 63°
b. <klm = 117°, <kln = 28°, and <nml = 63°
c. <klm = 63°, <kln = 28°, and <nml = 117°
d. <klm = 63°, <kln = 67°, and <nml = 117°

Explanation:

Step1: Use linear - pair property

$\angle KLO$ and the $152^{\circ}$ angle are a linear - pair. So, $\angle KLO=180^{\circ}-152^{\circ}=28^{\circ}$. $\angle LON$ and the $117^{\circ}$ angle are a linear - pair. So, $\angle LON = 180^{\circ}-117^{\circ}=63^{\circ}$.

Step2: Use properties of parallel lines and transversals

Since $JK\parallel ON$ and $OL$ is a transversal, $\angle KLO=\angle LON$ (alternate - interior angles). Also, since $KL\parallel OM$, $\angle KLM=\angle LON = 63^{\circ}$ (corresponding angles).

Step3: Find $\angle KLN$

$\angle KLN=\angle KLO = 28^{\circ}$ (alternate - interior angles as $KL\parallel OM$ and $OL$ is a transversal).

Step4: Find $\angle NML$

Since $ON\parallel KL$ and $OM$ is a transversal, $\angle NML=\angle LON = 63^{\circ}$ (corresponding angles).

Answer:

A. $\angle KLM = 63^{\circ},\angle KLN = 28^{\circ}$, and $\angle NML = 63^{\circ}$