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Name Class Date Lesson 7-6 Angles and Polygons Lesson Objective Common Core State Standard To find the angle measures of a polygon Geometry: 8.G.5 Vocabulary and Key Concepts For a polygon with n sides, the sum of the measures of the interior angles is (n 2 2)180° . Exterior angles are angles formed by a side and an extension of an adjacent side. All rights reserved. Polygon Angle Sum Interior angles are the angles inside a polygon at its vertices. Common Polygons Number of Sides Polygon Name Number of Sides Triangle 3 Octagon 8 Quadrilateral 4 Nonagon 9 Pentagon 5 Decagon 10 Hexagon 6 Dodecagon 12 7 Heptagon Example 1 Sum of the Interior Angle Measures Find the sum of the measures of the interior angles of an octagon. An octagon has 8 sides. (n 2)180 (8 ) 2 180° d Substitute 8 for n. 1,080 ° © Pearson Education, Inc., publishing as Pearson Prentice Hall. Polygon Name d Simplify. Quick Check 1. What is the sum of the measures of the interior angles of a heptagon? 900° 72 441198_C3_Ch7_WKbk_Ver-1.indd 72 Course 3 Lesson 7-6 Daily Notetaking Guide 10/10/12 5:46 PM Name Class Date Examples 2 Angle Measures of a Polygon Find the missing angle measure in the hexagon. 1478 Step 1 Find the sum of the measures of the interior angles of a hexagon. (n ( 2)180° 6 808 ) 1208 2 180° d Substitute 6 for n. 720° x8 d Simplify. 1368 1158 All rights reserved. Step 2 Write an equation. Let x 5 the missing angle measure. 120° 720° 80° 598° 720 122° 115° 147° 136° x x° x° d Write an equation. d Add. d Subtract 598° from each side. The missing angle measure is 122° . 3 Finding the Measure of an Exterior Angle /2 is an exterior angle of ABC. © Pearson Education, Inc., publishing as Pearson Prentice Hall. What is m/2 ? m/2 5 m/A 1 m/B B d Exterior angle of triangle 5 37° 1 90° d Substitute. 5 127° d Simplify. A 1 37° C 2 /2 measures 127°. Check By the angle sum of a triangle, m/1 5 180° 2 90° 2 37° 5 53°. /1 and /2 are supplementary, so m/2 5 180° 2 53° 5 127°.y Quick Check 2. A hexagon has five angles with measures of 142°, 84°, 123°, 130°, and 90°. What is the measure of the sixth angle? 1238 1308 848 151° 3. In RST, m/R 5 63° and m/S 5 84°. What is the measure of the exterior angle at vertex T ? 1428 x8 147° Daily Notetaking Guide 441198_C3_Ch7_WKbk_Ver-1.indd 73 Course 3 Lesson 7-6 73 10/10/12 5:46 PM