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WAEC Mathematics 2017 Paper

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Question : 25

Total: 49

Three exterior angles of a polygon are 30

^{\circ}

^{\circ}

^{\circ}

. If the remaining exterior angles are 46

^{\circ}

each, name the polygon.

decagon
nonagon
octagon
hexagon

Solution:

Concept:

The sum of all exterior angles of any polygon is

360^\circ

.

Explanation:

The three given exterior angles are

30^\circ

,

40^\circ

and

60^\circ

.

Their sum is

30^\circ + 40^\circ + 60^\circ = 130^\circ

.

Remaining sum of exterior angles is

360^\circ - 130^\circ = 230^\circ

.

Each remaining exterior angle is

46^\circ

.

Number of remaining angles is

\frac{230^\circ}{46^\circ} = 5

.

Total number of sides is

3 + 5 = 8

.

A polygon with 8 sides is called an octagon.

Answer:

C. octagon

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