Exploring Angles in Polygons

Mr. Cervone introduces a lesson on interior and exterior angles of polygons. He begins by solving a problem involving angle BCA and demonstrates how to apply the theorem that the sum of a triangle's interior angles is 180 degrees. The lesson progresses to proving the exterior angle theorem, which states that an exterior angle of a triangle is equal to the sum of its remote interior angles. The video concludes with an exploration of the relationships between interior and exterior angles in polygons, including a formula for calculating the sum of interior angles based on the number of sides.

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

• 90 degrees

• 180 degrees

• 270 degrees

• 360 degrees

If angle BCA is 180 minus 4x, and the sum of angles in a triangle is 180, what is the value of x when angle A is x and angle B is 120 degrees?

• 80 degrees

• 60 degrees

• 40 degrees

• 100 degrees

According to the exterior angle theorem, what does the exterior angle equal?

• Half the sum of the remote interior angles

• Twice the sum of the remote interior angles

• Difference of the remote interior angles

• Sum of the remote interior angles

How do you prove that the exterior angle of a triangle is equal to the sum of its remote interior angles?

• Using a statement-reason table

• Using algebraic manipulation

• Using geometric construction

• Using calculus

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

• 360 degrees

• 540 degrees

• 180 degrees

• 720 degrees

How many triangles can be drawn inside a hexagon to calculate its interior angles?

• Six

• Four

• Five

• Three

What is the formula to find the sum of the interior angles of a polygon with n sides?

• 180(n-2)

• n(180-2)

• 180n

• 360(n-2)

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

• They are none of the above

• They are complementary

• They are equal

• They are supplementary

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

• 360 degrees

• 540 degrees

• 180 degrees

• 720 degrees

How can the measure of each exterior angle of a regular polygon be calculated if the interior angle is unknown?

• 360 divided by the number of sides

• 180 minus the number of sides

• Sum of interior angles divided by the number of sides

• None of the above