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WAEC Mathematics 2016 Paper

Question : 24

Total: 49

Solution:

Concept:

The angle at the centre is twice the angle at the circumference subtending the same arc.

Angles around a point sum to

360^{\circ}

Explanation:

Let

\alpha

be the angle at the centre that subtends the same arc as

\angle XWZ = m^{\circ}

By the circle theorem:

\alpha = 2m^{\circ}

The two central angles,

\alpha

and

\angle XOZ = 10m^{\circ}

, together make a full turn around O.

\alpha + 10m^{\circ} = 360^{\circ}

Substitute

\alpha = 2m^{\circ}

2m^{\circ} + 10m^{\circ} = 360^{\circ}

12m^{\circ} = 360^{\circ}

m = \frac{360}{12} = 30

Answer:

m = 30

Correct option: A

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