Exploring Angles in Polygons

The video tutorial covers the concepts of interior and exterior angles in polygons. It begins with a definition of polygons and examples of shapes that are and are not polygons. The formula for calculating the sum of interior angles is introduced, followed by examples of its application to different polygons. The tutorial also demonstrates how to find missing angles within polygons. The concept of exterior angles is explained, emphasizing that their sum is always 360 degrees, regardless of the polygon's shape. The video concludes with examples of solving problems involving exterior angles.

What defines a polygon?

• An open figure made of line segments

• A shape with curved sides

• A figure with sides that do not intersect

• A closed figure with sides that intersect only at endpoints

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

• 180(n - 3)

• 360(n - 3)

• 360(n - 2)

• 180(n - 2)

How many degrees are the interior angles of a pentagon?

• 180 degrees

• 720 degrees

• 540 degrees

• 360 degrees

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

• 900 degrees

• 360 degrees

• 540 degrees

• 720 degrees

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

• 900 degrees

• 1080 degrees

• 720 degrees

• 1260 degrees

How do you calculate a missing angle in a polygon given the other angles?

• Add the given angles and subtract from 360

• Multiply the number of sides by 180

• Divide the sum of known angles by the number of sides

• Subtract the sum of known angles from the total interior angle sum

How many sides does a regular polygon have if the sum of its interior angles is 1800 degrees?

• 8 sides

• 14 sides

• 10 sides

• 12 sides

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

• The number of sides times 180

• 360 degrees

• 180 degrees

• The number of sides minus 360

If three exterior angles of a polygon are 50, 91, and 127 degrees, what is the fourth angle?

• 92 degrees

• 82 degrees

• 102 degrees

• 112 degrees

What is the value of Z if the exterior angles of a polygon are Z, Z+26, and 124 degrees?

• 105 degrees

• 115 degrees

• 95 degrees

• 125 degrees