Podcast
Questions and Answers
What is the sum of the interior angle measures of a 20-gon?
What is the sum of the interior angle measures of a 20-gon?
3,240
What is the measure of one interior angle of a regular 12-gon?
What is the measure of one interior angle of a regular 12-gon?
150
What is the value of x in the regular polygon below?
What is the value of x in the regular polygon below?
40
What is the measure of an exterior angle of a regular octagon?
What is the measure of an exterior angle of a regular octagon?
Signup and view all the answers
If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?
If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?
Signup and view all the answers
Study Notes
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge of polygon angle sum theorems with these flashcards. The quiz covers various types of polygons, including 12-gons and octagons, focusing on the calculation of interior and exterior angles. Enhance your understanding of geometric principles through these practice questions.