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JAMB Mathematics 2014 Question 26

Question 26

Angles and Polygons

In the figure above, KL∥NM, LN bisects ∠KNM. If angle KLN is 54° and angle MKN is 35°, calculate the size of angle KMN.

Diagram for this question
  1. A.19°
  2. B.91°
  3. C.89°
  4. D.37°
Show the answer and explanation

Answer: D (37°)

Explanation

Since KL∥NM, ∠LNM = ∠KLN = 54° (alternate angles). LN bisects ∠KNM, so ∠KNM = 2 × 54° = 108°. In triangle KMN, ∠KMN = 180° − 108° − 35° = 37°.