The sum of the interior angles of a regular polygon is 1440^\circ. What is the measure, in… — JAMB UTME

The sum of the interior angles of a regular polygon is $1440^\circ$ . What is the measure, in degrees, of one exterior angle of this polygon?

Answer: 36 degrees

The measure of one exterior angle of the polygon is

36^\circ

The sum of the interior angles of an

n

-sided polygon is given by

(n-2) \times 180^\circ

. Setting

(n-2) \times 180^\circ = 1440^\circ

gives

n-2 = 8

, so the polygon has

n = 10

sides (a decagon). The measure of each exterior angle of a regular polygon is

\frac{360^\circ}{n} = \frac{360^\circ}{10} = 36^\circ

Set up the equation for the sum of interior angles of an

n

-sided polygon.

(n - 2) \times 180^\circ = 1440^\circ

The sum of interior angles of any convex

n

-sided polygon is

(n - 2) \times 180^\circ

Solve for

n

, the number of sides.

n - 2 = \frac{1440}{180} = 8 \implies n = 10

Dividing the interior angle sum by

180^\circ

gives

n - 2

Calculate the measure of one exterior angle.

Exterior angle

= \frac{360^\circ}{10} = 36^\circ

The sum of exterior angles of any convex polygon is

360^\circ

, so each exterior angle of a regular polygon with

n

sides is

\frac{360^\circ}{n}

Relationship between interior angle sum, number of sides, and exterior angles of a regular polygon.

Question