# Polygon Angle Exploration

- Author:
- Ben Graber

Just as you can break a polygon into smaller shapes to find the total area of the polygon, you can also break the polygon down to find angle measurements. Use the applet to help answer the questions below.

a. How many triangles can you break a pentagon down into (using the vertices of the quadrilateral as the vertices of the triangles)? Does this work for ANY pentagon?
b. Based off your findings above, what will the total angle measurement of ALL the interior angles of a pentagon be?
c. How many triangles can you break a hexagon down into (using the vertices of the quadrilateral as the vertices of the triangles)? Does this work for ANY hexagon?
d. Based off your findings above, what will the total angle measurement of ALL the interior angles of a hexagon be?
e. Follow the pattern above. How many triangles could you break a heptagon down into? How about an octagon? Generalize this pattern; how many triangles could you break a polygon with

*n*sides down into? f. Using the formula you created, what will the total angle measurement of all the interior angles of a polygon with*n*sides? g. A regular polygon has side lengths and angles that have equal measurements. Using the total measurement of all the interior angles of a pentagon, what will the measurement of one angle in a regular pentagon be? h. How could you find the measurement of one interior angle in a regular polygon with*n*sides?