 ```SHAPE IT UP!!
A
D
C
B
B
C
A
E
D
A
F
B
E
D
C
B
A
C
G
F
D
E
Number of sides (n)
3
4
5
Number of Triangles
1
2
3
4
Sum of Angle
Measures
180
360
540
720
900
60
90
108
120
128.57
Measure of Each Angle
in a Regular Polygon
with n sides
6
7
5
1. Write an expression to represent the number of triangles formed by drawing
the diagonals of a polygon with n sides. __n-2_______
2. Explain how you derived the expression in #1.
There are different acceptable reasons, but students should realize that the number of
triangles, created by drawing each polygon’s diagonals, is two less than the number of sides.
3. Write an expression to represent the sum of the measures of the interior
angles of a polygon with n sides. ___(n-2)*180____________
4. Explain how you derived the expression in #3.
There are different acceptable answers, but students should realize that since the sum of the
measures of the angles in each triangle is 180 degrees, and there are (n-2) triangles, the sum of
the measure of the angles of the polygon is (n-2)*180__________________________________
5. Write an expression to represent the measure of each angle in a polygon with n
sides. ___[(n-2)*180] / n
6. Explain how you derived the expression in #5. There are different acceptable
answers, but students should realize that the measure of each angle in a regular polygon is the
sum of the measure of the angles divided by the number of angles, [(n-2)*180] / n.
```