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WAEC Mathematics 2018 Paper

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Question : 38

Total: 50

In the diagram, PS and RS are tangents to the circle centre O. ∠PSR = 70°, ∠POR = m, and ∠PSR =n. Find ( m + n ).

110 $^{\circ}$
135 $^{\circ}$
165 $^{\circ}$
225 $^{\circ}$

Solution:

Concept:

Use the tangent-radius property and the circle angle theorem.

Explanation:

Since

PS

and

RS

are tangents,

OP \perp PS

and

OR \perp RS

.

So

\angle OPS = 90^{\circ}

and

\angle ORS = 90^{\circ}

.

In quadrilateral

OPSR

, the sum of angles is

360^{\circ}

.

Therefore,

m + 90^{\circ} + 90^{\circ} + 70^{\circ} = 360^{\circ}

.

This gives

m = 110^{\circ}

.

The angle at the centre,

m

, subtends the same arc as the angle at the circumference,

n

.

Hence,

n = \frac{1}{2} \times m = \frac{1}{2} \times 110^{\circ} = 55^{\circ}

.

So,

m + n = 110^{\circ} + 55^{\circ} = 165^{\circ}

.

Answer:

165^{\circ}

Correct option: C.

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