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WAEC Mathematics 2010 Paper

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Question : 41

Total: 49

In the diagram, < ROS = 66^o and < POQ = 3x. some construction lines are shown. Calculate the value of x.

10^o
11^o
22^o
35^o

Solution:

Concept:

An angle bisector divides an angle into two equal parts.

Explanation:

From the diagram,

OP

bisects

\angle ROS

.

So,

\angle POS = \frac{1}{2} \times \angle ROS

.

Given

\angle ROS = 66^\circ

, we get:

\angle POS = \frac{1}{2} \times 66^\circ = 33^\circ

.

From the construction lines,

\angle POQ = \angle POS

.

Therefore,

\angle POQ = 33^\circ

.

But

\angle POQ = 3x

.

Hence,

3x = 33^\circ

.

Divide both sides by

3

:

x = \frac{33^\circ}{3} = 11^\circ

.

Answer:

x = 11^\circ

, which is option B.

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