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Polygons and their Angle Measures

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Polygons and their Angle Measures Essential Questions How do I identify and classify polynomials? How do I find the measures of interior and exterior angles of polygons? – PowerPoint PPT presentation

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Title: Polygons and their Angle Measures


1
Polygons and their Angle Measures
2
Essential Questions
  • How do I identify and classify polynomials?
  • How do I find the measures of interior and
    exterior angles of polygons?
  • How do I use measures of angles of polygons to
    solve problems?

3
  • Polygon- a plane figure that (1) is formed by 3
    or more segments, such that no two sides with a
    common endpoint are collinear and (2) each side
    intersects exactly 2 other sides , 1 at each
    endpoint.
  • Means the figure is closed and no sides cross
    over each other.
  • Vertex- the endpoints of each side
  • Think of them as the corner points!

4
Example
vertex
side
5
ExampleIs the figure a polygon?
yes
yes
no
no
6
  • Number of sides
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • 12
  • n
  • Type of polygon
  • Triangle
  • Quadrilateral
  • Pentagon
  • Hexagon
  • Heptagon
  • Octagon
  • Nonagon
  • Decagon
  • Dodecagon
  • N-gon

7
Special types of Polygons
  • Convex- no line that contains a side of a polygon
    goes through its interior
  • Concave- opposite of a convex
  • Equilateral- all sides are ?
  • Equiangular- all angles are ?
  • Regular polygon- equilateral and equiangular

8
  • Diagonal- a segment that joins 2 nonconsecutive
    vertices

A
segments AE and AD are diagonals
C
B
D
E
9
Interior Angles of a Quadrilateral
  • The sum of the measures of the interior ?s of a
    quad 360o.

A
B
A
1
2
m?1 m?2 m?3 m?4 360o
3
4
C
D
10
ExampleFind x
(
X
  • xx5555360
  • 2x110360
  • 2x250
  • X125

55o
)
X
11
Polygon Interior Angles Theorem
  • The sum of the measures of the interior angles of
    a convex n-gon is (n-2)180.

12
Corollary to the Polygon Interior Angles Theorem
  • The measure of each interior angle of a regular
    n-gon is

13
Example
  • Find the value of x in the diagram shown.

108146101113153x720
621 x 720
x 99
The measure of the 6th interior angle is 99!
14
Try This!
  • Find the value of x.

93º123º102º100ºxº 540º
418 x 540
x 122
15
Example
  • The measure of each interior angle of a regular
    polygon is 140. How many sides does the polygon
    have?

The polygon has 9 sides.
16
Try This!
  • The measure of each interior angle of a regular
    polygon is 165º. How many sides does the polygon
    have?

The polygon has 24 sides.
17
Polygon Exterior Angles Theorem
  • The sum of the measures of the exterior angles of
    a convex polygon, one angle at each vertex, is
    360º.

18
Corollary to the Polygon Exterior Angles Theorem
  • The measure of each exterior angle of a regular
    n-gon is

19
Example
  • Find the value of x.

2x?2x?4x?3x?x? 360?
12x 360
x 30
20
Example
  • Find the value of x.

x 360/7
x ? 51.43º
21
Try This!
  • Find the value of y.

y? y? 2y? 2y? 360?
6y 360
y 60
22
Summarizer
  • Explain in words how to find the measure of each
    interior angle and each exterior angle in a
    regular polygon.
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