Exploring Angles in Polygons

The video tutorial explains how to find the sum of interior angles in polygons without using a formula, by drawing diagonals to form triangles. It introduces the concept of n-gons and derives the angle sum formula. Key vocabulary related to polygons is discussed, including regular and convex polygons. The tutorial includes practice problems to apply the concepts and concludes with the exterior angles theorem.

What is an n-gon in the context of polygons?

• A polygon with a specific number of sides, denoted by 'n'

• A polygon with no sides

• A polygon that changes shape

• A polygon with infinite sides

How many triangles are formed when diagonals are drawn from one vertex in a hexagon?

• Five triangles

• Four triangles

• Three triangles

• Six triangles

How many triangles would a 20-sided polygon divide into when diagonals are drawn from one vertex?

• 20 triangles

• 22 triangles

• 18 triangles

• 17 triangles

Using the derived formula, what is the sum of the interior angles of a decagon?

• 1440 degrees

• 1800 degrees

• 1600 degrees

• 1200 degrees

What is the correct formula for finding the sum of the interior angles of a polygon?

• (Number of sides / 2) x 180

• (Number of sides x 2) - 180

• (Number of sides + 2) x 180

• (Number of sides - 2) x 180

What type of polygon is a regular polygon?

• A polygon that is concave

• A polygon with all sides and angles equal

• A polygon with no equal sides

• A polygon with only right angles

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

• 145 degrees

• 150 degrees

• 120 degrees

• 135 degrees

What is the name of a 7-sided polygon?

• Heptagon

• Nonagon

• Hexagon

• Decagon

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

• The number of sides times 360

• 180 degrees

• The number of sides times 180

• 360 degrees

If a polygon's interior angle sum is 1260 degrees, how many sides does it have?

• Eight sides

• Seven sides

• Nine sides

• Ten sides