Questions and Answers
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?
150
What is the value of x in the regular polygon below?
40
What is the measure of an exterior angle of a regular octagon?
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If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have?
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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.
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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.
