We saw that a vertex angle of a regular n-gon has measure degrees. If three regular pol...

We saw that a vertex angle of a regular n-gon has measure degrees. If three regular polygons surround a vertex, the three vertex angle measures must add to 360°. Therefore, if three regular polygons with a sides, b sides, and c sides surround a vertex we have the following.

a. Suppose one of the polygons is an equilateral triangle, so a = 3. Find all values for b and c that satisfy the equation.

b. Suppose one of the polygons is a square, so a = 4. Find all values for b and c that satisfy the equation.

c. Suppose one of the polygons is a regular pentagon, so a = 5. Find all values for b and c that satisfy the equation.

d. Suppose one of the polygons is a regular hexagon, so a = 6. Find all values for b and c that satisfy the equation.