1. 8.1 – Find Angle Measures in Polygons

2. 2 1 Interior Angle: Exterior Angle: Diagonal: Angle inside a shape 1
Angle outside
a shape 1
Line connecting two nonconsecutive vertices

3. triangle 1 180° # of sides Name of Polygon
# of triangles formed from 1 vertex
Sum of the measures of interior angles 3
triangle 1
180°

4. quadrilateral 2 360° # of sides Name of Polygon
# of triangles formed from 1 vertex
Sum of the measures of interior angles 4
quadrilateral 2
360°

5. pentagon 3 540° # of sides Name of Polygon
# of triangles formed from 1 vertex
Sum of the measures of interior angles 5
pentagon 3
540°

6. hexagon 4 720° # of sides Name of Polygon
# of triangles formed from 1 vertex
Sum of the measures of interior angles 6
hexagon 4
720°

7. 900° heptagon 5 octagon 6 1080° nonagon 7 1260° 8 decagon 1440° n-gon
# of sides
Name of Polygon
# of triangles formed from 1 vertex
Sum of the measures of interior angles 7 8 9 10 n
900°
heptagon 5
octagon 6
1080°
nonagon 7
1260° 8
decagon
1440°
n-gon
n – 2
180(n – 2)

8. The sum of the measures of the interior angles of a polygon are:_______________________
The measure of each interior angle of a regular n-gon is:
180(n – 2) n

9. Sum of Angles
Each angle
Interior
180(n – 2) n
180(n – 2)

10. 1. Find the sum of the measures of the interior angles of the indicated polygon.
180(7 – 2)
180(5)
900°
heptagon
Name __________________
Polygon Sum = __________
900°

11. 1. Find the sum of the measures of the interior angles of the indicated polygon.
180(30 – 2)
180(28)
5040°
30-gon
Name __________________
Polygon Sum = __________
5040°

12. 2. Find x.
180(n – 2)
180(5 – 2)
180(3)
540°
540°
x = 540
x = 540
x = 127°

13. 2. Find x.
180(n – 2)
180(4 – 2)
180(2)
360°
360°
x = 360
x = 360
x = 93°

14. 3. 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
2340°
n = 15

15. 3. 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

16. 4. Given the number of sides of a regular polygon, find the measure of each interior angle. 8 sides
180(8 – 2) 8
180(6) 8
1080 8 = = = =
135°
135° ?

17. 4. Given the number of sides of a regular polygon, find the measure of each interior angle. 18 sides
180(18 – 2) 18
180(16) 18
2880 18 = = = =
160°

18. 5. Given the measure of an 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 = 36n
144°
144°
10 = n

19. 5. Given the measure of an 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 = 72n
5 = n

20. Use the following picture to find the sum of the measures of the exterior angles.
ma =
70° d
120°
70°
110°
mb =
50° e
Sum of the exterior
angles = b
130°
mc =
110°
110° a
360°
md =
60°
me =
70°

21. 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

22. Sum of Angles
Each angle
Exterior
360° n
360°

23. 6. Find x.
x =
360
x = 360
x = 71°

24. 6. Find x.
x =
360
x = 360
x = 52°

25. 7. Find the measure of each exterior angle of the regular polygon.
12 sides
360° n
360° 12
30° = = ?

26. 7. Find the measure of each exterior angle of the regular polygon.
5 sides
360° n
360° 5
72° = =

27. 8. 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
60°
60°

28. 8. 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

29. MEMORIZE!!!!
Sum of Angles
Each angle
Interior
Exterior
180(n – 2) n
180(n – 2)
360° n
360°

30. HW Problem #24 180(n – 2) n 156 = 1 156n = 180n – 360 0 = 24n – 360
Section
Page #
Assignment
Spiral
8.1
#3-11 odd, 12, 15, 16, 19, 24, 25, 29
1-5
#24
180(n – 2) n
156 = 1
156n = 180n – 360
0 = 24n – 360
360 = 24n
15 = n