Exploring Angles in Polygons

Mr. Ray explains the concepts of interior and exterior angles in polygons, focusing on regular and convex polygons. He demonstrates how to calculate the sum of interior angles by dividing polygons into triangles and explains that the sum of exterior angles is always 360 degrees for convex polygons. The video includes practical examples and problem-solving techniques, emphasizing the relationship between interior and exterior angles.

What defines a regular polygon?

• Polygons with all sides and angles equal

• Polygons with only acute angles

• Polygons with varying side lengths

• Polygons with at least one right angle

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

• 180 degrees

• 360 degrees

• 720 degrees

• 540 degrees

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

• 270 degrees

• 90 degrees

• 360 degrees

• 180 degrees

How many triangles form a hexagon?

• Five triangles

• Six triangles

• Four triangles

• Three triangles

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

• Multiply the number of sides by 180

• Subtract two from the number of sides and multiply by 180

• Add two to the number of sides and multiply by 180

• Divide the number of sides by 180

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

• 540 degrees

• 360 degrees

• 180 degrees

• 720 degrees

What is the measure of one exterior angle of a regular 12-gon?

• 45 degrees

• 30 degrees

• 15 degrees

• 60 degrees

Why do exterior angles of a concave polygon not sum to 360 degrees?

• Because they include right turns

• Because they only include left turns

• Because they are always more than 180 degrees

• Because they are always less than 180 degrees

How many sides does a polygon have if its interior angles sum to 6660 degrees?

• 42 sides

• 40 sides

• 37 sides

• 35 sides

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

• They are equal

• They are unrelated

• They are supplementary

• They are complementary