7.2 Exploring Exterior Angles of Polygons Warm Up 1. Name the polygon by the number of its sides. Then tell whether the polygon is regular or irregular, concave or convex. 2. Find the sum of the interior angle measures of a convex 11-gon. 3. Find the measure of each interior angle of a regular 18-gon. 7.2 Exploring Exterior Angles of Polygons Objective: Determine the exterior angles of polygons. An exterior angle of a polygon is an angle formed by one side extended outside the polygon and the adjacent side of the polygon. An exterior angle is supplementary to the adjacent interior angle. 7.2 Exploring Exterior Angles of Polygons angles exterior ______ There are actually two __________ congruent at each vertex, but they are __________ because they are vertical angles. exterior angle and the Notice that the _________ interior ________angle adjacent to it are supplementary ____________; they add up to _____°. 180 exterior angle at each vertex of a To draw one ___________ extend polygon _______________ the side length of a polygon like a ray. Theorem 7.2: Exterior Angles Sum Theorem The sum of the exterior angles of a polygon, one at each vertex, is 360°. π π’π ππ πππ‘πππππ β π + π π’π ππ ππ₯π‘πππππ β π = 180°π π β 2 180° + π π’π ππππ₯π‘πππππ β π = 180°π 180°π β 360° + π π’π ππππ₯π‘πππππ β π = 180°π 0 + π π’π ππ ππ₯π‘πππππ β π = 180°π β 180°π + 360° π π’π ππ ππ₯π‘πππππ β π = 360° Examples: Use the information in the diagram to solve for x. 1. 2. 3. Fill in the blanks to describe the regular nonagon shown. a. Sum of the measures of the interior angles: b. Measure of each interior angle: c. Sum of the measures of the exterior angles: d. Measure of each exterior angle: 4. Find the measure of each interior and exterior angle.
© Copyright 2026 Paperzz