Test Index

WAEC Mathematics 2016 Paper

Question : 40

Total: 49

Solution:

Concept:

Angles in the same segment of a circle are equal.

Explanation:

Since

O

is the centre,

P, Q, R

and

S

lie on the circumference of the circle.

From the diagram,

\angle RPQ = 80^\circ

because

\angle RPQ

and

\angle QSR

are in the same segment, standing on chord

RQ

The ray

PR

divides

\angle QPS

into

\angle RPQ

and

\angle SPR

So,

\angle QPS = \angle RPQ + \angle SPR

Thus,

100^\circ = 80^\circ + \angle SPR

This gives

\angle SPR = 100^\circ - 80^\circ = 20^\circ

Now,

\angle SPR

and

\angle SQR

are in the same segment because both stand on chord

SR

Therefore,

\angle SQR = \angle SPR = 20^\circ

Answer:

20^\circ

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