NABTEB Mathematics 2024 Objective — Question 31

Question 31 of 50 from the National Business and Technical Examinations Board (NABTEB) Mathematics 2024 Objective paper, with the correct answer and a full explanation.

In the diagram, JKL is a tangent to the circle GHIK at K. ∠LKG=38° and ∠HIK=87°. Calculate the value of the angle marked x.

A. A. 93°Correct
B. B. 55°
C. C. 42°
D. D. 23°

Explanation

By the tangent-chord angle theorem, ∠LKG (tangent-chord angle) = angle in the alternate segment = ∠GHK = 38°. Using the cyclic quadrilateral property (opposite angles supplementary) together with the given ∠HIK=87°, the angle marked x works out to 93°.

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