ANGLES OF POLYGONS

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ANGLES OF POLYGONS

• SPI 3108.4.3     
• Identify, describe and/or apply the relationships
  and theorems involving different types of
  triangles, quadrilaterals and other polygons.

JIM SMITH JCHS
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POLYGONS
NOT POLYGONS
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CONCAVE
CONVEX
TRY THE PEGBOARD AND RUBBER BAND TEST
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NAMES OF POLYGONS

• SIDES
• TRIANGLE 3
• QUADRILATERAL 4
• PENTAGON 5
• HEXAGON 6
• HEPTAGON 7
• OCTAGON 8
• NONAGON 9
• DECAGON 10
• DODECAGON 12
• N GON N

SEE PAGE 46 IN TEXTBOOK
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INTERIOR ANGLE SUM OF CONVEX POLYGONS
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS
FROM ONE VERTEX
6 SIDES 4 TRIANGLES
6
INTERIOR ANGLE SUM
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS
FROM ONE VERTEX
4 SIDES 2 TRIANGLES
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INTERIOR ANGLE SUM
FIND THE NUMBER OF TRIANGLES FORMED BY DIAGONALS
FROM ONE VERTEX
8 SIDES
6 TRIANGLES
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INTERIOR ANGLE SUM

• EACH TRIANGLE HAS 180 DEGREES
• IF N IS THE NUMBER OF SIDES THEN
• (N 2 ) 180 INT ANGLE SUM

9
2
3
1
4
5
INT ANGLE SUM ( 5 2 ) 180
( 3 ) 180 540 DEGREES
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REGULAR POLYGONS

• REGULAR POLYGONS HAVE EQUAL SIDES AND EQUAL
  ANGLES SO WE CAN FIND THE MEASURE OF EACH
  INTERIOR ANGLE

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EACH INTERIOR ANGLE OF A REGULAR POLYGON
(N 2 ) 180 N
REMEMBER N NUMBER OF SIDES
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REGULAR HEXAGON
INT ANGLE SUM (6 2 ) 180 720
EACH INT ANGLE 720 120 6
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EXTERIOR ANGLE SUM
EXTERIOR ANGLE
THE MEASURE OF EACH EXTERIOR ANGLE OF A REGULAR
POLYGON IS 360 N
ALL POLYGONS HAVE AN EXTERIOR ANGLE SUM OF
360