* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Angles of a Polygon
Survey
Document related concepts
Technical drawing wikipedia , lookup
Tessellation wikipedia , lookup
Steinitz's theorem wikipedia , lookup
Shapley–Folkman lemma wikipedia , lookup
Approximations of π wikipedia , lookup
Integer triangle wikipedia , lookup
Multilateration wikipedia , lookup
Regular polytope wikipedia , lookup
Rational trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Perceived visual angle wikipedia , lookup
Trigonometric functions wikipedia , lookup
List of regular polytopes and compounds wikipedia , lookup
Euclidean geometry wikipedia , lookup
Transcript
Angles of a Polygon Diagonal of a polygon – A segment that connects any two nonconsecutive vertices. The number of triangles formed by drawing diagonals from one vertex of a polygon is always two less than the number of sides of the polygon, expressed as n-2. Angles of a Polygon Interior Angle Sum Theorem • The sum of the measures of the interior angles of a convex polygon with n sides is (n - 2)180. Since the angles in a regular polygon are congruent, you can find the measure of one interior angle of a regular polygon by dividing (n - 2)180 by the number of angles, n. The formula for this is: (n - 2)180 n A decorative window is designed to have the shape of a regular octagon. Find the sum of the measures of the interior angles of the octagon. Answer: 1080 The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon. Answer: The polygon has 10 sides. Find the measure of each interior angle. Answer: Angles of a Polygon Exterior Angle Sum Theorem • The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360. To find the measure of one exterior angle of a regular polygon, divide 360 by the number of sides. Find the measures of an exterior angle and an interior angle of convex regular hexagon ABCDEF. Answer: 60; 120