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WAEC Mathematics 2019 Paper

Question : 30

Total: 50

Solution:

Concept:

Angles of a triangle sum to

180^\circ

, and consecutive angles in a parallelogram are supplementary.

Explanation:

\triangle OST

|OS| = |OT|

, so it is isosceles.

Hence,

\angle OST = \angle OTS = 50^\circ

Therefore,

\angle SOT = 180^\circ - (50^\circ + 50^\circ) = 80^\circ

Since

POS

and

ROT

are straight lines,

\angle POR

is vertically opposite to

\angle SOT

So,

\angle POR = 80^\circ

In parallelogram

OPQR

\angle POR

is the angle at vertex

O

Consecutive angles of a parallelogram are supplementary, so

\angle OPQ = 180^\circ - 80^\circ = 100^\circ

Answer:

\angle OPQ = 100^\circ

— Option A.

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