In the diagram, {MN}//{PQ},

Correct Answer is : 100∘^{}∘

Correct Answer is : 100∘^{}∘

Test Index

WAEC Mathematics 2020 Paper

Question : 28

Total: 48

\overline{MN}

\overline{PQ}

Solution:

Concept:

\overline{MN} \parallel \overline{PQ}

and the line

\overline{NP}

acts as a transversal.

So, the alternate interior angles

\angle MNP

and

\angle NPQ

are equal.

Explanation:

Given:

\angle MNP = 2x

and

\angle NPQ = (3x - 50)^\circ

Since these are alternate interior angles, we write:

2x = (3x - 50)^\circ

Solve for

x

2x = 3x - 50

Bring like terms together:

50^\circ = 3x - 2x

x = 50^\circ

Now substitute

x = 50^\circ

into

\angle NPQ

\angle NPQ = 3x - 50^\circ

= 3(50^\circ) - 50^\circ

= 150^\circ - 50^\circ

= 100^\circ

Answer:

\angle NPQ = 100^\circ

The correct option is B.

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