Polygon Sum Theorem

Front

What is the Polygon Sum Theorem?

Back

The Polygon Sum Theorem states that the sum of the interior angles of a polygon with n sides is (n-2) × 180 degrees.

Front

What is the formula for the sum of exterior angles in a polygon?

Back

The sum of the exterior angles of any polygon is always 360 degrees.

Front

How do you calculate the measure of a single exterior angle in a regular polygon?

Back

To find the measure of a single exterior angle in a regular polygon, divide 360 degrees by the number of sides (n): 360/n.

Front

What is the measure of a single exterior angle in a 16-gon?

Back

22.5 degrees.

Front

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

Back

The interior angle and its corresponding exterior angle are supplementary, meaning they add up to 180 degrees.

Front

How do you find the sum of the interior angles of a polygon with 10 sides?

Back

Use the formula (n-2) × 180, where n is the number of sides: (10-2) × 180 = 1440 degrees.

Front

What is the sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180 degrees.

Front

If a polygon has 8 sides, what is the sum of its interior angles?

Back

The sum of the interior angles of an octagon (8 sides) is (8-2) × 180 = 1080 degrees.

Front

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

Back

In a regular hexagon, each interior angle measures 120 degrees.

Front

How do you determine the number of sides in a polygon if the sum of the interior angles is 720 degrees?

Back

Use the formula (n-2) × 180 = 720. Solving gives n = 6, so the polygon has 6 sides.