Exploring Interior and Exterior Angles

Mr. Robinson introduces the concepts of interior and exterior angles of polygons, starting with triangles. He explains the triangle angle sum theorem, followed by the polygon angle sum theorem, using examples to illustrate how to calculate the sum of interior angles in polygons. The video concludes with the remote exterior angle theorem, highlighting its utility in simplifying calculations.

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

• 180 degrees

• 90 degrees

• 270 degrees

• 360 degrees

What theorem is used to prove that the sum of the interior angles of a triangle is always 180 degrees?

• Polygon Angle Sum Theorem

• Triangle Angle Sum Theorem

• Remote Exterior Angle Theorem

• Linear Pair Theorem

What is a diagonal in the context of polygons?

• A line parallel to one of the sides

• A line connecting two non-adjacent vertices

• A line connecting a vertex to the center of the polygon

• A line connecting two adjacent vertices

How is the interior angle sum of a polygon calculated?

• Sum of the angles of all triangles formed within the polygon

• 180 degrees multiplied by (number of sides - 2)

• 360 degrees divided by the number of sides

• 180 degrees multiplied by the number of sides

What is the interior angle sum of a pentagon?

• 540 degrees

• 720 degrees

• 900 degrees

• 1080 degrees

How many triangles are formed by diagonals in a hexagon?

• Three

• Four

• Five

• Six

What is the interior angle sum of a seven-sided polygon?

• 900 degrees

• 1080 degrees

• 1260 degrees

• 1440 degrees

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

• 135 degrees

• 120 degrees

• 150 degrees

• 180 degrees

What does the Remote Exterior Angle Theorem state?

• The exterior angle is equal to the sum of the two opposite interior angles.

• The exterior angle is equal to the sum of the two adjacent interior angles.

• The exterior angle is supplementary to the adjacent interior angle.

• The exterior angle is equal to the sum of the two remote interior angles.

What property of triangles is used to prove the Remote Exterior Angle Theorem?

• Corresponding angles

• Alternate interior angles

• Complementary angles

• Supplementary angles