7-6 Angles and Polygons. Video Tutor Help Finding the angle measures of a polygonFinding the angle measures of a polygon (7-6) Finding the angle measures.

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Presentation transcript:

7-6 Angles and Polygons

Video Tutor Help Finding the angle measures of a polygonFinding the angle measures of a polygon (7-6) Finding the angle measures of a regular polygonFinding the angle measures of a regular polygon (7-6)

Video Tutor Help Finding the measure of an angle Exploring angles and transversals Identifying congruent triangles Using proportion to find unknown length in similar figures Finding the angle measures of a polygon Finding the angle measures of a regular polygon

7-6 Note Taking Guide 7-6 Practice 7-6 Guided Problem Solving 7-6 Worksheets

Chapter 7 Vocabulary (Electronic) Flash Cards Vocabulary Practice Vocabulary Graphic Organizer

7-6 Step-by-Step Examples Additional Lesson Examples

7-6 Problem of the Day 7-6 Lesson Quiz Lesson Readiness

Angles and Polygons LESSON 7-6 Find the sum of the measures of the interior angles of an octagon. An octagon has 8 sides. (n – 2) 180º = (8 – 2) 180º Substitute 8 for n. = 1,080ºSimplify. = (6) 180ºSubtract. The sum of the interior angles of an octagon is 1,080. Additional Examples

Example 6-3a Traffic Signs A stop sign is a regular octagon. What is the measure of one interior angle in a stop sign? Step 1 Find the sum of the measures of the angles. An octagon has 8 sides. Therefore,. Replace n with 8. Simplify. Step 2 Divide the sum by 8 to find the measure of one angle. The sum of the measures of the interior angles is 1080°. Answer: So, the measure of one interior angle in a stop sign is 135°. Find Angle Measure of a Regular Polygon

Angles and Polygons LESSON 7-6 Find the missing angle measure in the hexagon. Step 1 Find the sum of the measures of the interior angles of a hexagon. (n – 2) 180° = (6 – 2) 180° Substitute 6 for n. Simplify. = 720° Additional Examples

Angles and Polygons LESSON 7-6 (continued) Step 2 Write an equation. 720° = 120° + 115° + 136° + 80° + 147° + x° Write an equation. Let x = the missing angle measure. 720° = 598° + x° Add. 122° = x° Subtract 598º from each side. The missing angle measure is 122º. Additional Examples

Angles and Polygons A design on a tile is in the shape of a regular nonagon. Find the measure of each angle. LESSON 7-6 Each angle of a regular nonagon has a measure of 140°. (n – 2) 180° = (9 – 2) 180° Substitute 9 for n since a nonagon has 9 sides. = 1,260° Simplify. 1,260° ÷ 9 = 140° Divide the sum by the number of angles in a nonagon. Additional Examples