Practical Practice

1. Let's use our formula to confirm that the sum of interior angles in a hexagon is 720 degrees!

[i]Remember, the formula for the sum of the interior angles of a polygon is [/i][math]180^\circ\times\left(n-2\right)[/math][i], where [/i][math]n[/math][i] is the number of sides of a polygon[br][br][/i]Since we have a hexagon, we know that there are [b]6[/b] sides, and so the sum of the interior angles of a hexagon can be found by[br][br][center][math]180^\circ\times[/math]([color=#274e13][b]6[/b][math]-2[/math])[math]=720^\circ[/math][/color][/center]

2. Here's a dodecagon (dough-deck-uh-gon)! It has 12 sides. Find the sum of the interior angles of a dodecagon!

What should the sum of the interior angles of a dodecagon be?

[i]Remember that the formula we discovered was [/i][math]180^\circ\times\left(n-2\right)[/math][i], where [/i][math]n[/math][i] is the number of sides of the polygon[/i]

[math]2160^\circ[/math] [math]150^\circ[/math] [math]1800^\circ[/math] [math]1440^\circ[/math]

This may look like a circle, but it is in fact a 65-gon! (That's a lot of sides!) After a certain point, we stop giving special names to polygons and just name them by how many sides they have.

Find the sum of the interior angles of a 65-gon!

[i]You may need to bust out a calculator for this one[/i]

[math]11,340^\circ[/math] [math]56,700^\circ[/math] Too many! [math]11,700^\circ[/math]