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WAEC Mathematics 2019 Paper

Question : 40

Total: 50

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Solution:

Concept:

By the tangent-chord theorem, the angle between tangent

RT

and chord

RQ

equals the angle in the alternate segment.

Explanation:

Given

\angle QRT = 52^\circ

, this is the angle between tangent

RT

and chord

RQ

So the angle subtended by chord

RQ

at the circumference is

\angle QPR = 52^\circ

\triangle PQR

, we know

\angle PQR = 70^\circ

and

\angle QPR = 52^\circ

Using the angle sum of a triangle:

x = 180^\circ - (70^\circ + 52^\circ)

x = 180^\circ - 122^\circ = 58^\circ

Answer:

x = 58^\circ

Correct option: B.

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