6.1.1 Properties and Attributes of Polygons (continued)
The measure of the exterior angles of a regular hexagon is determined in this example. According to the Polygon Exterior Angle Sum Theorem, the sum of the interior angles is 360°. The hexagon has 6 sides. Since the hexagon is regular, all the interior angles are congruent. The size of each angle is 360°/6 = 60°. The measures of unknown exterior angles of a polygon are determined in this example. The measures of the angles of the quadrilateral are given as multiples of an unknown x . According to the Polygon Exterior Angle Sum Theorem, the sum of the exterior angles is 360°. Equate the sum of the expressions given for the angle measures to 360°. Solve for x . The value of x is 36°. This is the measure of the exterior angles at S and R . The measures of the other two angles can be determined by substitution.
Example 5 Problem-Solving Application
The measure of an exterior angle of a regular pentagon is determined in this application example. The building shape is given as a regular pentagon. According to the Polygon Exterior Angle Sum Theorem, the sum of the exterior angles is 360°. Since the pentagon is regular, all the exterior angles are congruent. The size of each angle is 360°/5 = 72°.
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