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WAEC Mathematics 2013 Paper

Question : 40

Total: 48

Solution:

Concept:

Use parallel lines, the isosceles triangle formed by two radii, and the inscribed angle theorem.

Explanation:

Since

OM \parallel XZ

, the alternate angles give:

\angle OZX = \angle ZOM = 25^\circ

\triangle OXZ

OX = OZ

because both are radii of the circle.

So,

\angle OXZ = \angle OZX = 25^\circ

Thus, the central angle is:

\angle XOZ = 180^\circ - (25^\circ + 25^\circ) = 130^\circ

The inscribed angle

\angle XYZ

subtends the same chord

XZ

as the central angle

\angle XOZ

Therefore:

\angle XYZ = \frac{1}{2} \times 130^\circ = 65^\circ

Answer:

65^\circ

(Option D).

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