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BECE Mathematics 2023 Paper

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Question : 26

Total: 40

In the diagram,

A B

C D

A G E

80^{\circ}

C F G=5 k

C F E=r

. Use the information to answer the question below.

Find the value of

k

$16^{\circ}$
$20^{\circ}$
$80^{\circ}$
$160^{\circ}$

Solution:

Concept:

Use corresponding angles and the linear pair property of angles on a straight line.

Explanation:

Since

AB \parallel CD

, the corresponding angles are equal.

Therefore,

r = 80^{\circ}

.

Angles

CFE

and

CFG

lie on the straight line

EFG

, so their sum is

180^{\circ}

.

Thus,

r + 5k = 180^{\circ}

.

Substitute

r = 80^{\circ}

:

80^{\circ} + 5k = 180^{\circ}

5k = 180^{\circ} - 80^{\circ}

5k = 100^{\circ}

Divide both sides by

5

:

k = \frac{100}{5} = 20^{\circ}

Answer:

k = 20^{\circ}

, which is option B.

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