Angles in Polygons
Mar 27, 2015
Angles in Polygons
Sums of Interior Angles
Triangle Quadrilateral Pentagon
Heptagon OctagonHexagon
= 2 triangles = 3 triangles
= 4 triangles= 5 triangles = 6 triangles
Convex Polygon
# of Sides # of Triangles
Sum of Interior Angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
n-gon
3
4
5
6
7
8
n
1
2
3
4
5
6
n – 2
180360
540
720
900
1080
180•(n – 2)
Find the measure of the missing angle in the figure below
100135
70x
135 + 100 + 70 + x =
quadrilateral
360305 + x = 360
-305 -305x = 55
m1 =1
2
3
110
(5x - 5)
(4x + 15)
(8x - 10)
pentagon5x - 5 + 4x + 15 + 8x - 10 + 110 + 90 = 540
17x + 200= 540 -200 -200
17x = 340
x = 20 17 17
5(20) - 5
= 95
Find m1.
12
34
5 6
Exterior Angles
Interior Angles
Sum of Interior Angles =
Sum of Interior & Exterior Angles =
180
12
34
5 6
180
180
180
540
Sum of Exterior Angles = 360 540- 180=
Sums of Exterior Angles
180•3 = 540
180
180
180
180
Sum of Interior Angles =
Sum of Interior & Exterior Angles =
360 720
Sum of Exterior Angles = 360 720- 360=
Sums of Exterior Angles
180•4 = 720
Sum of Exterior Angles
180 180
180
180
180
Sum of Interior Angles =
Sum of Interior & Exterior Angles =
Sum of Exterior Angles = 360 900- 540=
900
540°
180•5 = 900
Sum of Exterior Angles
Sum of Interior Angles = Sum of Interior & Exterior Angles =
Sum of Exterior Angles =
180
180180
180
180
180
360 1080- 720=
1080720°
180•6 = 1080
Sums of Exterior Angles
Polygon # of Sides
Interior +
Exterior
Interior Angles
Exterior Angles
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
180
360
540
720
540
720
900
1080
360
360
360
360Sum of Exterior Angles
is always 360!
Angles of Regular Polygons
Sum of the Interior Angles
Sum of the Exterior Angles
Each Interior Anglen
Each Exterior Angle n
180(n – 2)
Always 360!
180(n – 2)
360
Find the sum of the measures of the interior angles of a regular dodecagon.
180•(n – 2) = 180•(12 – 2)
n = 12
= 180•(10)= 1800 all 12 angles
= 150180012
each angle
What is the measure of each angle?
The sum of the interior angles of a convex polygon is 1440.
How many sides does the polygon have?
180•(n – 2) = 1440
180n = 1800+ 360 +360
180 180
n = 10 10 sides
180n – 360 = 1440
Exterior Angles
What is the measure of each exterior angle of a regular hexagon?
360
6 sides
6= 60
The measure of each exterior angle of a regular polygon is 20. How many
sides does it have?
20360 = 18
The measure of each interior angle of a regular polygon is 120. How many
sides does it have?
60360 = 6
180 - 120 = 60
exterior angle
Find the sum of the interior angles of a 100-gon!
Find the sum of the exterior angles of a 100-gon.
Find the measure of each interior angle of a 100-gon.
Find the measure of each exterior angle of a 100-gon.