Polygon Angle Sum Theorem

Front

What is the Polygon Angle Sum Theorem?

Back

The Polygon Angle Sum Theorem states that 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 number of sides in a polygon if the sum of its interior angles is known?

Back

To find the number of sides (n) of a polygon when the sum of its interior angles is known, use the formula: n = (Sum of interior angles / 180°) + 2.

Front

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

Back

The measure of each exterior angle of a regular polygon can be calculated using the formula: 360° / n, where n is the number of 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

How do you find the measure of one interior angle of a regular polygon?

Back

To find the measure of one interior angle of a regular polygon, use the formula: (Sum of interior angles / n) = [(n - 2) × 180°] / n.

Front

If a polygon has 15 sides, what is the sum of its interior angles?

Back

The sum of the interior angles of a 15-sided polygon is (15 - 2) × 180° = 2340°.

Front

What is the measure of one interior angle of a regular hexagon?

Back

The measure of one interior angle of a regular hexagon is 120°.

Front

If a regular octagon has 8 sides, what is the measure of each exterior angle?

Back

Each exterior angle of a regular octagon is 360° / 8 = 45°.

Front

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

Back

The interior and exterior angles of a polygon are supplementary, meaning they add up to 180°.

Front

How many sides does a polygon have if the sum of its interior angles is 1080°?

Back

The polygon has 10 sides, calculated as (1080° / 180°) + 2 = 10.