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question 3
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which are the correct measures for <nok and <jon?
select one:
a. <nok = 38°, <jon = 35°
b. <nok = 35°, <jon = 36°
c. <nok = 28°, <jon = 63°
d. <nok = 35°, <jon = 82°

Explanation:

Step1: Use angle - sum property of parallelogram

In parallelogram $JKLM$, $\angle KLM = 152^{\circ}$, and $\angle KLM+\angle KJM = 180^{\circ}$ (adjacent angles of a parallelogram are supplementary), so $\angle KJM=28^{\circ}$. Also, $\angle JOP = 117^{\circ}$.

Step2: Find $\angle JON$

$\angle JON = 180^{\circ}-\angle JOP=180 - 117=63^{\circ}$ (linear - pair of angles).

Step3: Find $\angle NOK$

In $\triangle JON$, we know that the sum of angles in a triangle formed by the diagonals and sides of the parallelogram. Since $\angle KJM = 28^{\circ}$ and using angle - relationships in the parallelogram and the given angles, $\angle NOK = 28^{\circ}$ (alternate - interior or related angle properties in parallelogram).

Answer:

C. $\angle NOK = 28^{\circ},\angle JON = 63^{\circ}$