MATHEMATICS

JAMB 2005 - Question 26

Mathematics 2005 JAMB Past Questions - Question 26: The sum of the interior angle of a regular polygon is 1800. calculate the size of one exterior angle of the polygon.

The sum of the interior angle of a regular polygon is 1800. calculate the size of one exterior angle of the polygon.
A:
B:
C:
D:
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Correct Answer

A

Explanation

To find the size of one exterior angle of a regular polygon, we can use the formula:Exterior angle = 360° / Number of sidesSince the sum of the interior angles of a polygon with n sides is given by the formula:Sum of interior angles = (n - 2) * 180°We can equate the sum of the interior angles to 1800°:(n - 2) * 180° = 1800°Simplifying the equation:n - 2 = 10n = 12Therefore, the polygon has 12 sides. Now we can find the size of one exterior angle:Exterior angle = 360° / 12Exterior angle = 30°So, the size of one exterior angle of the polygon is 30 degrees.