Angles in Polygons

1
Angles in Polygons

• 3.6
• Matt, James, Eric, Robert

2
Sum of Interior Angles of a Polygon

• The sum of the measures of the interior angles of
  a polygon with n sides is 180(n-2)
• N the number of sides the polygon has.
• Ex. Triangle has 3 sides, so 180(3-2) 180(1)
  180 º which is the sum of the interior angles of
  the triangle

3
Interior Angle of a Regular Polygon Formula

• 180(n-2)/n
• Ex. A square has 4 sides, so 180(4-2)/4 360/4
  90º

4
Sum of Exterior Angles of a Polygon

• The sum of the measures of the exterior angles of
  a polygon is 360 º
• Ex. In a equilateral triangle, each exterior
  angle is 120 º. 120120120 360 º

120 º
120 º
120 º
5
Finding the Number of Sides of a Regular Polygon
Given Interior Angle

• First, you need one of the interior angles.
• Then, you subtract it from 180 to get the
  exterior angle.
• When you get the exterior angle you divide 360 by
  it and your answer should be the number of sides
  the polygon has.
• Ex. I.A.60, 180-60120, 360/1203 sides

6
Finding the Number of sides of a Regular Polygon
Given Exterior Angle

• First, you need one of the exterior angles.
• Then, you divide 360 by it
• The answer should be the number of sides the
  polygon has.
• Ex. E.A.90, 360/904 sides

7
Finding the Measure of an Angle of a Polygon
Given the Angle Measures as Mathematical
Expressions

• First, combine the like terms of all the
  expressions.
• Then, find out the sum of all the interior
  angles.
• After this is done, all you do is the algebra and
  find out what the x equals.
• Then you plug x into each problem.

8
Example
4x3x2xx 360 10x 360 10x/10360/10 X 36
4(36) 144
3(36) 108
4x
3x
2x
x
2(36) 72
1(36) 36