Question

12-gon

Sum of interior angles and the measure of each interior angle for the given regular polygons

Answer 1

• The sum of the interior angles = 1800

• Interior angle = 150°

Explanation:

we know that the sum of all the Exterior Angles of a polygon is 360°.

i.e.

• Sum of all the Exterior Angles of a polygon = 360°

The formula to find the Exterior angle:

• Exterior angle = 360° / n

As the total number of sides = n = 12

so

Exterior angle = 360° / 12 = 30

so

Every exterior angle = 30°

• As the Interior Angle and Exterior Angle tend to be measured from the same line, hence they add up to 180°.

i.e.

Interior Angle = 180° − Exterior Angle

= 180° - 30°

= 150°

The formula for calculating the sum of interior angles is:

( n − 2 ) × 180° = (12-2) × 180

= 10 × 180

= 1800

SECOND METHOD TO DETERMINE INTERIOR ANGLE MEASURE

Interior angle = sum of interior angle ÷ number of sides

= 1800 ÷ 12

= 150

Hence,

• The sum of the interior angles = 1800

• Interior angle = 150°