Polygon Angle Sum Theorems Quiz

Polygon-Angle Sum Theorems

• The sum of interior angle measures in a polygon can be calculated using the formula: (n - 2) × 180°, where n is the number of sides.
• For a 20-gon, this formula yields a total of 3,240° for interior angles.

Regular Polygons

• In a regular 12-gon, each interior angle measures 150°. This is derived from the formula: (n - 2) × 180° ÷ n.

Calculating Unknowns in Polygons

• In problems involving regular polygons, variables such as x can represent the measure of an unknown angle. For a particular regular polygon situation, the value of x is determined to be 40°.

Exterior Angles of Polygons

• The measure of an exterior angle in a regular octagon is 45° and can be calculated using the formula: 360° ÷ n, where n indicates the number of sides.

Finding the Number of Sides Based on Exterior Angle

• If the exterior angle of a regular polygon measures 24°, the number of sides can be calculated as 360° ÷ 24°, resulting in a polygon with 15 sides.