Question

which are the correct measures for <ojk, <jko, and <jok? select one: a. <ojk = 117°, <jko = 36°, and <jok = 37° b. <ojk = 152°, <jko = 18°, and <jok = 10° c. <ojk = 117°, <jko = 28°, and <jok = 35° d. <ojk = 102°, <jko = 28°, and <jok = 50°

Explanation:

Step1: Use property of parallel - lines

Since $JK\parallel ON$ and $\angle PON = 117^{\circ}$, then $\angle OJK=\angle PON = 117^{\circ}$ (corresponding angles).

Step2: Use angle - sum property of triangle

In $\triangle OJK$, we know that the sum of interior angles of a triangle is $180^{\circ}$. Let's check each option.
For option a: $117^{\circ}+36^{\circ}+37^{\circ}=190^{\circ}
eq180^{\circ}$.
For option b: $152^{\circ}+18^{\circ}+10^{\circ}=180^{\circ}$, but $\angle OJK = 117^{\circ}
eq152^{\circ}$.
For option c: $117^{\circ}+28^{\circ}+35^{\circ}=180^{\circ}$ and $\angle OJK = 117^{\circ}$.
For option d: $102^{\circ}+28^{\circ}+50^{\circ}=180^{\circ}$, but $\angle OJK = 117^{\circ}
eq102^{\circ}$.

Answer:

C. $\angle OJK = 117^{\circ},\angle JKO = 28^{\circ}$, and $\angle JOK = 35^{\circ}$