In the previous exercise we made a conjecture about the sum of the measures of the angles
S in an
n-sided .
S=(n−2)⋅180
Let's test it on other polygons. We can try it on a heptagon, an octagon, and a nonagon.
Heptagon
A heptagon is a
7-sided polygon. Therefore, we will substitute
n=7 in our formula.
S=(n−2)⋅180
▼
Substitute 7 for n and evaluate
S=900
According to our conjecture, the sum of the measures of the angles in a heptagon is
900. Let's draw it and calculate this sum without the formula.
We divided the heptagon into
5 triangles. The sum of the measures of the angles in each of them is
180. Therefore, the sum of the measures of the angles in the heptagon is
5 times
180.
5⋅180=900
As we can see, it is the same as the sum we got using our conjecture, so we can tell that it works in this case.
Octagon
An octagon is an
8-sided polygon. Therefore, we will substitute
n=8 in our formula.
S=(n−2)⋅180
▼
Substitute 8 for n and evaluate
S=1080
Now, let's draw it and calculate this sum without the formula.
We divided the octagon into
6 triangles. The sum of the measures of the angles in each of them is
180. Therefore, the sum of the measures of the angles in the octagon is
6 times
180.
6⋅180=1080
It is the same as the sum we got using our conjecture, so we can tell that it also works in this case.
Nonagon
A nonagon is a
9-sided polygon. Therefore, we will substitute
n=9 in our formula.
S=(n−2)⋅180
▼
Substitute 9 for n and evaluate
S=1260
Now, let's draw it and calculate this sum without the formula.
As we can see, it divides into
7 triangles. The sum of the measures of the angles in each of them is
180. Therefore, the sum of the measures of the angles in the nonagon is
7 times
180.
7⋅180=1260
It is the same as the sum we got using our conjecture, so we can tell that it also works in this case.
Conclusion
Our conjecture worked for each polygon we tried it on. Therefore, we can conclude that it holds true.