Polygon Angle Sum Theorem

Front

What is the Polygon Angle Sum Theorem?

Back

The sum of the interior angles of a polygon with n sides is given by the formula (n - 2) × 180°.

Front

How do you calculate the sum of the interior angles of a polygon with 8 sides?

Back

(8 - 2) × 180° = 6 × 180° = 1080°.

Front

What is the measure of each interior angle in a regular pentagon?

Back

The sum of the interior angles of a pentagon is (5 - 2) × 180° = 540°. Since it is regular, each angle is 540° / 5 = 108°.

Front

What is the measure of each exterior angle in a regular polygon?

Back

Each exterior angle of a regular polygon can be found using the formula 360° / n, where n is the number of sides.

Front

If a polygon has 12 sides, what is the sum of its interior angles?

Back

(12 - 2) × 180° = 10 × 180° = 1800°.

Front

What is the relationship between interior and exterior angles of a polygon?

Back

The interior angle and exterior angle at each vertex of a polygon are supplementary, meaning they add up to 180°.

Front

How do you find the number of sides of a polygon if the sum of its interior angles is 720°?

Back

Using the formula (n - 2) × 180° = 720°, we can solve for n: n - 2 = 720° / 180°; n - 2 = 4; n = 6. The polygon has 6 sides.

Front

What is the sum of the exterior angles of any polygon?

Back

The sum of the exterior angles of any polygon is always 360°, regardless of the number of sides.

Front

Calculate the sum of the interior angles of a regular hexagon.

Back

(6 - 2) × 180° = 4 × 180° = 720°.

Front

What is the measure of each exterior angle of a regular octagon?

Back

360° / 8 = 45°.