Final answer:
Using the Alternate Interior Angles Theorem, angle ∠MONK is found to be 59 degrees because it is an alternate interior angle to ∠LKI, which is also 59 degrees. The correct answer is option a).
Step-by-step explanation:
Given that JL and MO are parallel lines, we can determine the measure of angles based on their relationship with other angles. The question pertains to the field of geometry, which involves parallel lines and angles formed when a transversal intersects parallel lines.
Specifically, it asks for the measurement of angle ∠MONK given that lines JL and MO are parallel and angle ∠LKI is 59°. To determine the measurement of ∠MONK, we can use the Alternate Interior Angles Theorem, which states that when a transversal intersects two parallel lines.
Alternate interior angles are equal. Since ∠LKI and ∠MONK are alternate interior angles and JL is parallel to MO, ∠MONK must also measure 59°, which means the correct answer is a) 59°.