November 9, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by - Interior and Exterior Angles of Polygons.

In this mini-lesson, you will learn with the help of some examples and video presentation about the interior and exterior angles. Any polygon has as many corners as it has sides. Each corner has several angles and the two most important ones are- interior angle and exterior angle.

It explains how to find sum of all the interior angles and exterior angles of a polygon. An exterior angle of a polygon is the angle formed by any side and a line extended from an adjacent side. E.g. if the interior angle of triangle is 30° then its exterior angle is 150°. The sum of interior angles of a triangle is 180°, therefore, in case of isosceles right triangle the degree of angle measure would be 45°, 45°, and 90°. Take case of pentagon, which can be formed by joining three triangles and thus sum of interior angles is (3*180° = 540°). Thus each interior angle of a regular polygon is 108°.

Remember the fact that if the number of sides of a polygon is increased by 1, sum of the interior angles is increased by 180°. According to Polygon Interior-Angle-Sum theorem, sum of the measures of the interior angles of a polygon with n sides is equal to (n-2)180°. For example, sum of interior angles of a triangle is (3-2)180°, it comes to 180°. In general, interior angle of a regular polygon with n sides is given by: (n-2)180°/n. For example, the interior angle of a regular hexagon can be worked out by (6 - 2)180°/6 = 120°. Similarly the according to exterior Angle-Sum Theorem, the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. Remember also the exterior angle is the supplementary angle to the interior angle.

In this mini-lesson, you will learn with the help of some examples and video presentation about the interior and exterior angles. Any polygon has as many corners as it has sides. Each corner has several angles and the two most important ones are- interior angle and exterior angle.

It explains how to find sum of all the interior angles and exterior angles of a polygon. An exterior angle of a polygon is the angle formed by any side and a line extended from an adjacent side. E.g. if the interior angle of triangle is 30° then its exterior angle is 150°. The sum of interior angles of a triangle is 180°, therefore, in case of isosceles right triangle the degree of angle measure would be 45°, 45°, and 90°. Take case of pentagon, which can be formed by joining three triangles and thus sum of interior angles is (3*180° = 540°). Thus each interior angle of a regular polygon is 108°.

Remember the fact that if the number of sides of a polygon is increased by 1, sum of the interior angles is increased by 180°. According to Polygon Interior-Angle-Sum theorem, sum of the measures of the interior angles of a polygon with n sides is equal to (n-2)180°. For example, sum of interior angles of a triangle is (3-2)180°, it comes to 180°. In general, interior angle of a regular polygon with n sides is given by: (n-2)180°/n. For example, the interior angle of a regular hexagon can be worked out by (6 - 2)180°/6 = 120°. Similarly the according to exterior Angle-Sum Theorem, the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. Remember also the exterior angle is the supplementary angle to the interior angle.

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Geometry. Click on the video below to go through it. If you like it, you can buy our online course in Geometry by clicking here.

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Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.