Test Index

BECE Mathematics 2021 Paper

© africaexams.com

Question : 18

Total: 40

In the diagram, line

A B

is parallel to line

P D

. Find the value of

x

$20^{\circ}$
$80^{\circ}$
$100^{\circ}$
$120^{\circ}$

Solution:

Concept:

Since

AB \parallel PD

, alternate angles are equal. Also, the sum of angles in a triangle is

180^\circ

.

Explanation:

On the straight line through

C

, we have

120^\circ + \angle DCB = 180^\circ

.

So

\angle DCB = 180^\circ - 120^\circ = 60^\circ

.

Because

AB \parallel PD

, alternate angles are equal, so

\angle OBA = \angle DCB = 60^\circ

.

Now in

\triangle ABO

, the given angle at

A

is

20^\circ

.

Using the sum of angles in a triangle:

x + 60^\circ + 20^\circ = 180^\circ

.

x + 80^\circ = 180^\circ

.

x = 180^\circ - 80^\circ = 100^\circ

.

Answer:

x = 100^\circ

, which is Option C.

© africaexams.com

Go to Question:

Prev Question

Next Question