NABTEB Mathematics 2022 Objective — Question 36

Question 36 of 50 from the National Business and Technical Examinations Board (NABTEB) Mathematics 2022 Objective paper, with the correct answer and a full explanation.

The diagram shows triangle MNR inscribed in a circle and PQ is a tangent line. If angle MRN=41 degrees and angle PMR=141 degrees, find angle QNR.

• A. 39 degrees
• B. 80 degreesCorrect
• C. 110 degrees
• D. 141 degrees

Explanation

angle PMR = angle MRN + angle RNM (exterior angle equals sum of two opposite interior angles): 141=41+RNM, so RNM=100 degrees. RNM+QNR=180 (angles on a straight line): 100+QNR=180, so QNR=80 degrees.

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