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)
The sum of the measures of the interior angles of a polygon are:_______________________
180(n – 2)

8. The measure of each interior angle of a regular n-gon is:

9. Find the sum of the measures of the interior angles of the indicated polygon.
180(18 – 2)
180(16)
2880°

10. Find the sum of the measures of the interior angles of the indicated polygon.
180(30 – 2)
180(28)
5040°

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

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

13. 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

14. 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

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

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

17. 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 = 36n
10 = n

18. 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 = 72n
5 = n

19. Use the following picture to find the sum of the measures of the exterior angles.
ma =
110°
mb =
60°
Sum of the exterior
angles =
mc =
100°
360°
md =
90°

20. The sum of the exterior angles, one from each
vertex, of a polygon is: ____________________
360°

21. The measure of each exterior angle of a
regular n-gon is: _________________________
360° n

22. Find x.
x =
360
x = 360
x = 71°

23. Find x.
x =
360
x = 360
x = 52°

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

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

26. 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

27. 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

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

29. HW Problem
8.1
3-15 odd, 16, 19, 24, 25, 29, 31
#13
13. Find x.
Ans:
180(n – 2)
x+143+2x =1080
180(8 – 2)
3x = 1080
180(6)
x = 88.33°
1080°