Question

if the measure of a central angle of a regular polygon is 60 find the measure of each of its interior angles

Answer 1

Definition: The angle subtended at the center of the polygon by one of its sides.

Try this Adjust the number of sides of the polygon below, or drag a vertex to note the central angle of the polygon.

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Regular Polygon case

The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon. If you were to draw a line from any two adjacent vertices to the center, they would make the central angle. Because the polygon is regular, all central angles are equal. It does not matter which side you choose.

All central angles would add up to 360° (a full circle), so the measure of the central angle is 360 divided by the number of sides. Or, as a formula:

central angle =

360

n

degrees

Answer 2

The Measure Of Each Interior Angle Is 120°

GIVEN

The central angle of a regular polygon = 60°

TO FIND

Measure OF its interior angles.

SOLUTION

We can simply solve the above problem as follows -

We know that a regular polygon is a 2 Dimensional figure that has sides of more than 3.

In a polygon, angles, as well as sides, are congruent.

Formula to calculate the central angle of a polygon,

= 360°/n

where n = number of sides.

Central angle = 60°

So,

60 = 360/n

n = 360/60 = 6 sides.

so, the polygon is a hexagon.

We know that,

The sum of interior angles of a polygon = (n-2)180

Therefore, the measure of each interior angle = (n-2)180/n

we know

n = 6.

So,

the measure of each interior angle =

$\frac{(6 - 2)180}{6}$

$= \frac{4 \times 180}{6}$

= 720/6

= 120°

Hence, the measure of each interior angle is 120°

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