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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 Sum of triangles angles Triangle 3 1 180° Quad Pentagon Hexagon n-gon n
  • 4. Polygon # of Sides # of Sum of triangles angles Triangle 3 1 180° Quad 4 2 2·180= 360° Pentagon 5 3 3·180= 540° Hexagon 6 4 4·180= 720° 10·180= Dodecagon 12 10 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 BM #34-35 n
  • 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. n • interior + exterior = 180n° interior = ( n − 2)180° or 180n − 360° So, 180n − 360 + exterior = 180n 1 −360 + exterior = 0 2 exterior = 360° 5 3 4
  • 9. BM #34 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?
  • 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. BM #35 Example 2: • Find the measure of each angle in a regular 11-gon.
  • 12. Ex. 2 solution: • (n-2)180=(11-2)180 • 9•180=1620° • 1620÷11=147.3°
  • 13. BM #36 Example 3: • The measure of each exterior angle of a regular polygon is 40°. How many sides does the polygon have?
  • 14. Ex. 3 Solution: • 360÷40=9 • 9 sides
  • 15. Assignment: #22 Polygon Worksheet #23 3.5 WS (p. 301)