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BECE Mathematics 2018 Paper

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Question : 17

Total: 40

In the diagram,

\overline{Q P}

\overline{S T}

Q P R=68^{\circ}

S R T=40^{\circ}

Use the information to answer the question below:

Find the value of angle TSR.

$40^{\circ}$
$68^{\circ}$
$72^{\circ}$
$112^{\circ}$

Solution:

Concept:

When two parallel lines are cut by a transversal, alternate interior angles are equal.

Explanation:

In the diagram,

\angle QPR

and

\angle TSR

are alternate interior angles because

\overline{QP} \parallel \overline{ST}

and the slanted line through

P

,

R

, and

S

acts as the transversal.

Therefore, alternate angles are equal:

\angle TSR = \angle QPR.

Given:

\angle QPR = 68^{\circ}.

So:

\angle TSR = 68^{\circ}.

Hence, the required value of angle

TSR

is

68^{\circ}

.

Answer:

68^{\circ}

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