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WAEC Mathematics 2013 Paper

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Question : 38

Total: 48

In the diagram, PQRS is a rhombus and < PSQ = 35º. Calculate the size of < PRQ

65^o
55^o
45^o
35^o

Solution:

Concept:

In a rhombus, diagonals bisect the interior angles, and adjacent angles are supplementary.

Explanation:

In rhombus

PQRS

, diagonal

QS

bisects

\angle PSR

.

Given

\angle PSQ = 35^\circ

, so

\angle PSR = 2 \times 35^\circ = 70^\circ

.

Adjacent angles in a rhombus are supplementary.

Thus,

\angle SRQ = 180^\circ - 70^\circ = 110^\circ

.

Diagonal

PR

bisects

\angle SRQ

.

So,

\angle PRQ = \frac{1}{2} \times 110^\circ = 55^\circ

.

Answer:

55^\circ

, i.e. Option B.

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