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WAEC Mathematics 2024 Paper

Question : 45

Total: 50

In the diagram $\overline{TU}$ is a tangent to the circle SPQR at P. If $\angle$ PTS = 44º, $\angle$ SQP = 35º, find $\angle$ PST

Solution:

Concept:

The alternate segment theorem and the angle sum of a triangle are used.

Explanation:

Given:

\overline{TU}

is a tangent at

P

\angle PTS = 44^\circ

, and

\angle SQP = 35^\circ

By the alternate segment theorem, the angle between tangent

TP

and chord

SP

equals the angle subtended by chord

SP

in the alternate segment.

Therefore,

\angle SPT = \angle SQP = 35^\circ

\triangle TSP

, the sum of angles is

180^\circ

So,

\angle PST = 180^\circ - \angle PTS - \angle SPT

Thus,

\angle PST = 180^\circ - 44^\circ - 35^\circ = 101^\circ

Answer:

\angle PST = 101^\circ

, which is option A.

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