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WAEC Mathematics 2011 Paper

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Question : 46

Total: 47

In the diagram /Pq//TS//TU, reflex angle QPS = 245^o angle PST = 115^o, , STU = 65^o and < RPS = x. Find the value of x

80^o
70^o
60^o
50^o

Solution:

Concept:

Angles at a point and corresponding angles formed by parallel lines.

Explanation:

The angles around point

P

add up to

360^\circ

.

So,

245^\circ + \angle QPR + x = 360^\circ

.

This gives

\angle QPR + x = 360^\circ - 245^\circ = 115^\circ

.

From the parallel lines,

\angle QPR = \angle STU = 65^\circ

because they are corresponding angles.

Substitute:

65^\circ + x = 115^\circ

.

Therefore,

x = 115^\circ - 65^\circ = 50^\circ

.

Answer:

x = 50^\circ

Correct option: D.

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