466 CHAPTER 8 Geometry Table 8.2 Sides Triangles Sum of the Measures of the Interior Angles 3 1 = 1(180°) 180° 4 2 = 2(180°) 360° 5 3 = 3(180°) 540° 6 4 = 4(180°) 720° If we continue this procedure, we can see that for an n-sided polygon the sum of the measures of the interior angles is − n( 2)180°. Sum of Interior Angles of Polygons 1 Sum of the Measures of Interior Angles The sum of the measures of the interior angles of an n-sided polygon is − n( 2)180°. Example 1 Angles of a Regular Decagon A regular decagon (see the figure in the margin) is a 10-sided figure with all sides having the same length and all interior angles having the same measure. Determine a) the measure of an interior angle. b) the measure of exterior 1. Solution a) Using the formula − n( 2)180°, we can determine the sum of the measures of the interior angles of the regular decagon. = − = ⋅ = Sum (10 2)180° 8 180° 1440° The measure of an interior angle of a regular polygon can be determined by dividing the sum of the interior angles by the number of angles. For a regular decagon, = = Measure of one interior angle 1440° 10 144° b) Since 1 is the supplement of an interior angle, m 1 180° 144° 36° = − = 7 Now try Exercise 43 To discuss area in the next section, we must be able to identify various types of triangles and quadrilaterals. The following is a summary of certain types of triangles and their characteristics.
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