11'1 Angle Measures in Polygons

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11.1 Angle Measures in Polygons

• p. 661

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If all the ?s in a ? add up to 180o and all the
?s in a quadrilateral add up to 360o, what about
a pentagon?
How about a hexagon?
2 180 3600
3 180 540o
4 180 720o
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Thm 11.1 Polygon Interior ?s thm.

• The sum of the measures of the interior ?s of a
  convex n-gon is 180(n-2).
• Remember n is the number of sides.

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Ex What is the sum of the measures of the
interior ?s of a dodecagon?

• First, how many sides does a dodecagon have?
• n 12
• 180(12-2)
• 180(10)
• 1800o

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Ex Find the value of x.

• Sum of all ?s is 540o
• 114105102135456o
• 540 456 84o
• So, x 84

114o
xo 135o
105o
102o
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Corollary to thm 11.1

• The measure of each interior ? of a regular n-gon
  is
• This means the measure of ONE ? ONLY!!!

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Ex The measure of each interior ?of a regular
polygon is 165o. How many sides does the polygon
have?

• 180(n-2) 165n
• 180n-360 165n
• -360 -15n
• 24 n
• 24 sides

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Thm 11.2 Polygon Exterior ?s thm

• The sum of the measures of the exterior ?s of a
  convex polygon, one at each vertex, is 360o.
• m?1 m?2 m?3 m?4 m?5 360o

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1
3
5
4
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Ex Solve for y.
y
2y
2y
y

• 2y y 2y y 360
• 6y 360
• y 60o

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Corollary to thm 11.2

• The measure of each exterior ? of a regular n-gon
  is

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Ex Solve for x.

• n 6
• 360/n x
• 360/6 x
• 60o x

xo
This is a regular hexagon.
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Assignment