McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
Extend: Geometry Software Lab, Two-Dimensional Figures
Continue to next subchapter

Exercise 9 Page 66

In the previous exercise we made a conjecture about the sum of the measures of the angles in an -sided polygon.
Let's test it on other polygons. We can try it on a heptagon, an octagon, and a nonagon.

Heptagon

A heptagon is a -sided polygon. Therefore, we will substitute in our formula.
Substitute for and evaluate
According to our conjecture, the sum of the measures of the angles in a heptagon is Let's draw it and calculate this sum without the formula.
We divided the heptagon into triangles. The sum of the measures of the angles in each of them is Therefore, the sum of the measures of the angles in the heptagon is times
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 -sided polygon. Therefore, we will substitute in our formula.
Substitute for and evaluate
Now, let's draw it and calculate this sum without the formula.
We divided the octagon into triangles. The sum of the measures of the angles in each of them is Therefore, the sum of the measures of the angles in the octagon is times
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 -sided polygon. Therefore, we will substitute in our formula.
Substitute for and evaluate
Now, let's draw it and calculate this sum without the formula.
As we can see, it divides into triangles. The sum of the measures of the angles in each of them is Therefore, the sum of the measures of the angles in the nonagon is times
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.