Exploring Interior and Exterior Angles of Polygons

The video tutorial covers the concepts of interior and exterior angles of polygons. It begins by defining polygons and distinguishing them from non-polygon shapes. The tutorial explains how to calculate the sum of interior angles using the number of triangles that can be formed within a polygon. It introduces a formula for finding the sum of interior angles based on the number of sides. The video also discusses regular polygons, where all sides and angles are congruent, and how to calculate the measure of each interior angle. Finally, it explains the concept of exterior angles, showing that their sum is always 360 degrees, regardless of the polygon's shape.

Which of the following is NOT a characteristic of polygons?

• Can include curved lines

• Formed by three or more line segments

• All sides are straight lines

• Must be closed figures

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

• Number of sides minus two, multiplied by 180

• Number of sides plus two, multiplied by 180

• Number of sides multiplied by 180

• Number of sides divided by 180

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

• 1080 degrees

• 360 degrees

• 540 degrees

• 720 degrees

What defines a regular polygon?

• All sides and angles are congruent

• Only angles are congruent

• No sides or angles are congruent

• Only sides are congruent

How do you find the measure of each interior angle of a regular pentagon?

• Add 2 to the number of sides, multiply by 180, then divide by 5

• Divide the sum of interior angles by 5

• Multiply the number of sides by 180 and divide by 5

• Subtract 2 from the number of sides, multiply by 180, then divide by 5

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

• 360 degrees

• 720 degrees

• 180 degrees

• 540 degrees

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

• 90 degrees

• 60 degrees

• 30 degrees

• 120 degrees

If the exterior angle of a regular polygon is 15 degrees, how many sides does it have?

• 30 sides

• 36 sides

• 24 sides

• 12 sides

If the exterior angle of a regular polygon is 40 degrees, how many sides does the polygon have?

• 6 sides

• 9 sides

• 12 sides

• 15 sides

How many sides does a polygon have if each exterior angle measures 12 degrees?

• 15 sides

• 20 sides

• 30 sides

• 40 sides