Angles in a Polygon Examples

What is the sum of the angles in a dodecagon?

A dodecagon has 12 sides.

We can find the sum of all the interior angles by using the formula (n - 2) × 180°. In case you forgot, n stands for the number of sides.

When we plug 12 in for n, we get:
(12 - 2) × 180° = 1800°

The sum of the interior angles of a dodecagon is 1800°.

What is the measure of each angle in a regular nonagon?

A nonagon has 9 sides. Using our formula, .

If we divide that into nine congruent angles, each angle will be:

Find the missing angle.

A triangle has 180°. If we add the measures of angles I and J and subtract from 180, we get:

Find the measurement of angle Q

This is a hexagon. The total number of degrees equals:

If we add up the measures of the other five angles

Now, subtract that total from 720, and

Find the missing angles in this isosceles trapezoid.

Since this is an isosceles trapezoid, angles I and L are congruent. In addition, angles J and K are congruent, so