Question

I need help For a regular n-gon: a. What is the sum of the measures of its angles? b. What is the measure of each angle? c. What is the sum of the measures of its exterior angles, one at each vertex? d. What is the measure of each exterior angle? e. Find the sum of your answers to parts b and d. Explain why this sum makes sense.

Answer 1

sum of exterior angles=360
each exterior angle of a regular polygon of n sides=360/n
each interior angle=180-360/n
\[=180\left( \frac{ n-2 }{n } \right)\]
sum of interior angles\[=n \times180( \frac{n-2 }{n })\]