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BECE Mathematics 2022 Paper

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Question : 18

Total: 40

In the diagram,

A B

D E

A B C = 81^{\circ}

D C E = 20^{\circ}

Use the information to answer the question below:

What is the value of

x

$\;\; A .20^{\circ}$
$\;\; 61^{\circ}$
$81^{\circ}$
$\;\; 101^{\circ}$

Solution:

Concept:

When parallel lines are cut by a transversal, the alternate angles formed are equal.

Explanation:

Here,

AB \parallel DE

.

Line

BC

acts as a transversal between the parallel lines

AB

and

DE

.

From the diagram,

\angle ABC

and

\angle CDE

are alternate angles.

Therefore,

\angle ABC = \angle CDE

.

The angle marked

x

is

\angle CDE

.

Given

\angle ABC = 81^\circ

, we get

x = 81^\circ

.

The value of

\angle DCE = 20^\circ

is not required to find

x

.

Answer:

x = 81^\circ

So, the correct option is C.

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