angles of polygons
DESCRIPTION
Angles of Polygons. Find the sum of the measures of the interior angles of a polygon Find the sum of the measures of the exterior angles of a polygon. This scallop resembles a 12-sided polygon with diagonals drawn from one of the vertices. SUM OF MEASURES OF INTERIOR ANGLES. - PowerPoint PPT PresentationTRANSCRIPT
Angles of Polygons• Find the sum of the measures of the interior angles of a
polygon• Find the sum of the measures of the exterior angles of a
polygon
This scallop resembles a 12-sided polygon with diagonals drawn from one of the vertices.
SUM OF MEASURES OF INTERIOR ANGLES
Polygons with more than 3 sides have diagonals.
Quadrilateral
SUM OF MEASURES OF INTERIOR ANGLES
Polygons with more than 3 sides have diagonals.
Pentagon
SUM OF MEASURES OF INTERIOR ANGLES
Hexagon
Polygons with more than 3 sides have diagonals.
SUM OF MEASURES OF INTERIOR ANGLES
Heptagon
Polygons with more than 3 sides have diagonals.
SUM OF MEASURES OF INTERIOR ANGLES
Octagon
Polygons with more than 3 sides have diagonals.
Theorem 8.1Interior Angle Sum Theorem
If a convex polygon has n sides then the sum S of the measures of its interior angles is:
S = 180(n - 2)
EXAMPLE 1
N = 5S = 180(n – 2) = 180(5 – 2) or 540
Find the sum of the interior angles of the pentagon.
Convex Polygons
No. of sides n Name Angle Sum Sum ÷ n
3 triangle 180° 60°
4 quadrilateral 360° 90°
5 pentagon 540° 108°
6 hexagon 720° 120°
7 heptagon 900° 129°
8 octagon 1080° 135°
9 nonagon 1260° 140°
10 decagon 1440° 144°
What is the exterior angle of each regular polygon? Is the total 360°in each case?
(4 – 2) x 180° = 360°360 – 245 = 115°
(5 – 2) x 180° = 540°540 – =
Interior Angles of Polygons
y122o
112o
100o
130o
136o z
134o 126o
136o
125o
125o
108o
Find the unknown angles below.
75°
100°
70°
x
120°
75°w 90°
(6 – 2) x 180° = 720°720 – =
(7 – 2) x 180° =
120°
Interior Angles of Polygons
Septagon/Heptagon Decagon Hendecagon
Dodecagon Hexadecagon Icosagon
Nonagon
900°/128.6°
Calculate the angle sum and interior angle of each of these regular polygons.
1 2 4
5 6 7
3
7 sides 9 sides 10 sides 11 sides
12 sides 16 sides 20 sides
EXAMPLE 2Find the measure of each interior angle
2x° 2x°
x° x°
n = 4
180(4 – 2) or 360
Sum of interior angles is
x
x
xxxx
DmCmBmAm
60
6360
22360
360
A
B C
D
Exterior Angle TheoremThe exterior angle of a triangle is equal to the sum of the remote interior angles.
exterior angle
A
B C D
i.e. ACD = ABC + BAC
remote interior angles
Exterior Angles of Polygons
Theorem 8.1Exterior Angle Sum Theorem
If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360°
1
2
3
4
5
36054321 mmmmm