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WAEC Mathematics 2017 Paper

Question : 38

Total: 49

Solution:

Concept:

Equal adjacent angles on a straight line can be doubled to form two larger angles whose sum is

180^\circ

Explanation:

Since

XY

is a straight line, the sum of angles on one side of line

XY

180^\circ

Let

\angle POQ = x

and

\angle ROY = y

Given

\angle POX = \angle POQ

, ray

OP

bisects

\angle XOQ

\angle XOQ = 2x

Given

\angle ROY = \angle QOR

, ray

OR

bisects

\angle QOY

\angle QOY = 2y

Now,

\angle XOQ + \angle QOY = 180^\circ

Therefore,

2x + 2y = 180^\circ

Factor out 2:

2(x + y) = 180^\circ

Divide both sides by 2:

x + y = 90^\circ

Thus,

\angle POQ + \angle ROY = 90^\circ

Answer:

90^\circ

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