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- 1. 3.5- Part 2 Angle Measures in Polygons
- 2. Investigation: Sum of the interior angles 1. Draw examples of 4-sided, 5-sided, and 6-sided polygons. In each polygon, draw all the diagonals from 1 vertex. 2. Complete the table on the next slide. What is the pattern in the sum of the measures of the interior angles in any convex n-gon?
- 3. Polygon # of Sides # of triangles Sum of angles Triangle 3 1 180° Quad Pentagon Hexagon n-gon n
- 4. Polygon # of Sides # of triangles Sum of angles Triangle 3 1 180° Quad 4 2 2·180= 360° Pentagon 5 3 3·180= 540° Hexagon 6 4 4·180= 720° Dodecagon 12 10 10·180= 1800 n-gon n n-2 (n-2)180°
- 5. Polygon Interior Angles Theorem The sum of the interior angles of a convex n-gon is (n-2)•180°. One angle in a regular n-gon: n − 2( )•180 nBM #34-35
- 6. Exterior Angles
- 7. Polygon Exterior Angle Theorem The sum of the measures of the exterior angles of a convex n-gon is 360°. BM #36
- 8. 1 2 3 4 5 n • interior +exterior =180n° interior = n − 2( )180° or 180n − 360° So, 180n − 360 + exterior = 180n −360 + exterior = 0 exterior = 360°
- 9. Example 1: • A heptagon has 4 interior angles that measure 160° each and two interior angles that are right angles. What is the measure of the other interior angle? BM #34
- 10. Ex. 1 Solution: • (n-2)180=interior sum • (7-2)180=5•180=900° • 4•160+2•90=640+180=820° • 900-820=80°
- 11. Example 2: • Find the measure of each angle in a regular 11-gon. BM #35
- 12. Ex. 2 solution: • (n-2)180=(11-2)180 • 9•180=1620° • 1620÷11=147.3°
- 13. Example 3: • The measure of each exterior angle of a regular polygon is 40°. How many sides does the polygon have? BM #36
- 14. Ex. 3 Solution: • 360÷40=9 • 9 sides
- 15. Assignment: #22 Polygon Worksheet #23 3.5 WS (p. 301)

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