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WAEC Mathematics 2016 Paper

Question : 23

Total: 49

\overline{PF}

\overline{QT}

\overline{RG}

Solution:

Concept:

The sum of interior angles of a triangle is

180^\circ

, and alternate or vertically opposite angles formed by intersecting lines are equal.

Explanation:

Let

\angle PSQ = x

From the diagram,

\angle RST = 22^\circ

Using vertically opposite angles and alternate angles,

\angle SQP = \angle RST = 22^\circ

Now in

\triangle PSQ

\angle PSQ + \angle SPQ + \angle SQP = 180^\circ

Substitute the known values:

x + 113^\circ + 22^\circ = 180^\circ

Simplify:

x + 135^\circ = 180^\circ

Therefore:

x = 180^\circ - 135^\circ = 45^\circ

Answer:

\angle PSQ = 45^\circ

, so the correct option is B.

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