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JAMB Mathematics 2013 Paper

Question : 33

Total: 47

In the diagram given, find the value of x.

Solution:

Concept:

Isosceles triangle angle property and exterior angle theorem.

Explanation:

\triangle CDE

, sides

CD

and

CE

are equal, so the base angles are equal.

Thus,

\angle CDE = \angle CED = 15^\circ

Then,

\angle ECD = 180^\circ - (15^\circ + 15^\circ) = 150^\circ

The angle

110^\circ

and

x

are the two opposite interior angles of the small triangle.

The exterior angle

\angle ECD

equals the sum of these opposite interior angles:

x + 110^\circ = 150^\circ

So,

x = 150^\circ - 110^\circ = 40^\circ

Answer:

x = 40^\circ

Correct option: B.

40^\circ

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