In the diagram, {QP} is parallel to {ST}, angle QPR=68^{} and angle SRT=40^{}. Use the information to answer the question below: Find the value of angle PQR.

Correct Answer is : 72∘72^{}72∘

Correct Answer is : 72∘72^{}72∘

Test Index

BECE Mathematics 2018 Paper

Question : 16

Total: 40

\overline{QP}

\overline{ST}

QPR=68^{\circ}

SRT=40^{\circ}

PQR

Solution:

Concept:

Vertically opposite angles are equal, and the sum of the angles in a triangle is

180^{\circ}

Explanation:

The two straight lines intersect at

R

So,

\angle TRS

and

\angle PRQ

are vertically opposite angles.

Therefore,

\angle PRQ = 40^{\circ}

\triangle PQR

, we have:

\angle QPR = 68^{\circ}

and

\angle PRQ = 40^{\circ}

Using the angle sum of a triangle:

\angle QPR + \angle PRQ + \angle PQR = 180^{\circ}

68^{\circ} + 40^{\circ} + \angle PQR = 180^{\circ}

108^{\circ} + \angle PQR = 180^{\circ}

\angle PQR = 180^{\circ} - 108^{\circ} = 72^{\circ}

Answer:

\angle PQR = 72^{\circ}

, so the correct option is C.

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