Post on 17-Dec-2015
transcript
8.1 – Find Angle Measures in Polygons
Interior Angle:
Exterior Angle:
Diagonal:
Angle inside a shape
Angle outsidea shape
Line connecting two nonconsecutive vertices
1 2
2
1
# of sides
Name of Polygon
# of triangles formed from 1
vertex
Sum of the measures of
interior angles
3 1 180°triangle
# of sides
Name of Polygon
# of triangles formed from
1 vertex
Sum of the measures of
interior angles
4 quadrilateral 2 360°
# of sides
Name of Polygon
# of triangles formed from
1 vertex
Sum of the measures of
interior angles
5 pentagon 3 540°
# of sides
Name of Polygon
# of triangles formed from
1 vertex
Sum of the measures of
interior angles
6 hexagon 4 720°
# of sides
Name of Polygon
# of triangles formed from
1 vertex
Sum of the measures of
interior angles
7
8
9
10
n
5 900°
6 1080°
7 1260°
8 1440°
n – 2 180(n – 2)
heptagon
octagon
nonagon
decagon
n-gon
The sum of the measures of the interior angles of a polygon are:_______________________180(n – 2)
The measure of each interior angle of a regular n-gon is:
180(n – 2) n
Find the sum of the measures of the interior angles of the indicated polygon.
18-gon
180(n – 2)
180(18 – 2)180(16)
2880°
Find the sum of the measures of the interior angles of the indicated polygon.
30-gon
180(n – 2)
180(30 – 2)180(28)
5040°
Find x.
180(n – 2)
180(5 – 2)180(3)
540°
x + 90 +143 + 77 + 103 = 540
x + 413 = 540
x = 127°
Find x.
180(n – 2)
180(4 – 2)180(2)
360°
x + 87 + 108 + 72 = 360
x + 267 = 360
x = 93°
Given the sum of the measures of the interior angles of a polygon, find the number of sides.
2340°
180(n – 2) = 2340
180n – 360 = 2340
180n = 2700
n = 15
Given the sum of the measures of the interior angles of a polygon, find the number of sides.
6840°
180(n – 2) = 6840
180n – 360 = 6840
180n = 7200
n = 40
Given the number of sides of a regular polygon, find the measure of each interior angle.
8 sides
180(n – 2) n
180(8 – 2) 8
180(6) 8
= =1080 8
=
135°=
Given the number of sides of a regular polygon, find the measure of each interior angle.
18 sides
180(n – 2) n
180(18 – 2) 18
180(16) 18
= =2880 18
=
160°=
Given the measure of each interior angle of a regular polygon, find the number of sides.
144°
180(n – 2) n
144=
1
144n = 180n – 360
0 = 36n – 360
360 = 36n10 = n
Given the measure of each interior angle of a regular polygon, find the number of sides.
108°
180(n – 2) n
108=
1
108n = 180n – 360
0 = 72n – 360
360 = 72n5 = n
Use the following picture to find the sum of the measures of the exterior angles.
ma =
mb =
mc =
md =
Sum of the exterior angles =
110°
60°
100°
90°360°
The sum of the exterior angles, one from each
vertex, of a polygon is: ____________________360°
The measure of each exterior angle of a
regular n-gon is: _________________________
360° n
Find x.
x + 137 + 152 = 360
x + 289 = 360
x = 71°
Find x.
x + 86 + 59 + 96 + 67 = 360
x + 308 = 360
x = 52°
Find the measure of each exterior angle of the regular polygon.
12 sides
360° n
= 360° 12
= 30°
Find the measure of each exterior angle of the regular polygon.
5 sides
360° n
= 360° 5
= 72°
Find the number of sides of the regular polygon given the measure of each exterior angle.
60°
360° n
= 60°1
60n = 360
n = 6
Find the number of sides of the regular polygon given the measure of each exterior angle.
24°
360° n
= 24°1
24n = 360
n = 15
Sum of Angles Each angle
Interior
Exterior
180(n – 2) n180(n – 2)
360° n360°
HW Problem8.1 510-512 3-15 odd, 16, 19, 24, 25, 29, 31
#1313. Find x.
180(n – 2)
180(8 – 2)
180(6)
1080°
x+143+2x+152+116+125+140+139=1080
3x + 815 = 1080
Ans:
x = 88.33°