3.5- Part 2
Angle Measures in
Polygons
Investigation: Sum of the
interior angles
1. Draw examples of 4-sided, 5-sided,
and 6-sided polygons. In each
polygon, dra...
Polygon # of Sides # of
triangles
Sum of
angles
Triangle 3 1 180°
Quad
Pentagon
Hexagon
n-gon n
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 ...
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-g...
Exterior Angles
Polygon Exterior Angle
Theorem
The sum of the measures
of the exterior angles of a
convex n-gon is 360°.
BM #36
1
2
3
4
5
n • interior +exterior =180n°
interior = n − 2( )180° or 180n − 360°
So, 180n − 360 + exterior = 180n
−360 + ext...
Example 1:
• A heptagon has 4 interior
angles that measure 160° each
and two interior angles that are
right angles. What i...
Ex. 1 Solution:
• (n-2)180=interior sum
• (7-2)180=5•180=900°
• 4•160+2•90=640+180=820°
• 900-820=80°
Example 2:
• Find the measure of each
angle in a regular 11-gon.
BM
#35
Ex. 2 solution:
• (n-2)180=(11-2)180
• 9•180=1620°
• 1620÷11=147.3°
Example 3:
• The measure of each exterior
angle of a regular polygon
is 40°. How many sides
does the polygon have?
BM
#36
Ex. 3 Solution:
• 360÷40=9
• 9 sides
Assignment:
#22 Polygon Worksheet
#23 3.5 WS (p. 301)
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Geo 3.5 b_poly_angles_notes

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Geo 3.5 b_poly_angles_notes

  1. 1. 3.5- Part 2 Angle Measures in Polygons
  2. 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. 3. Polygon # of Sides # of triangles Sum of angles Triangle 3 1 180° Quad Pentagon Hexagon n-gon n
  4. 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. 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. 6. Exterior Angles
  7. 7. Polygon Exterior Angle Theorem The sum of the measures of the exterior angles of a convex n-gon is 360°. BM #36
  8. 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. 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. 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. 11. Example 2: • Find the measure of each angle in a regular 11-gon. BM #35
  12. 12. Ex. 2 solution: • (n-2)180=(11-2)180 • 9•180=1620° • 1620÷11=147.3°
  13. 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. 14. Ex. 3 Solution: • 360÷40=9 • 9 sides
  15. 15. Assignment: #22 Polygon Worksheet #23 3.5 WS (p. 301)
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