1. **State the problem:** Given quadrilateral KLMN with KL parallel to NM, LN bisects angle KNM, angle KLN = 54°, and angle MKN = 35°. Find angle KMN. 2. **Understand the properties:** Since KL // NM and LN bisects angle KNM, we can use alternate interior angles and angle bisector properties. 3. **Identify angles:** Let angle KNM = 2x since LN bisects it, so each part is x. 4. **Use triangle KLN:** In triangle KLN, sum of angles = 180°. Given angle KLN = 54°, angle LNK = x (part of bisected angle), and angle KNL = 180° - 54° - x. 5. **Use triangle MKN:** Angles are MKN = 35°, KNM = 2x, and KMN = y (unknown). Sum of angles in triangle MKN: 35° + 2x + y = 180°. 6. **Use parallel lines property:** Since KL // NM, angle KLN = angle MKN + angle KMN (alternate interior angles), so 54° = 35° + y. 7. **Solve for y:** $$y = 54° - 35° = 19°$$ 8. **Answer:** Angle KMN = 19°. --- **Final answer:** 19° (option a)