Question

Find the measure of one interior angle in a regular 16-gon. Do not round the answer.

Answer 1

157.5°

Explanation:

We can calculate the sum of all the interior angles of an n-sided polygon, just like this:

`180\cdot(n-2)`

In this case it is 16 sides, therefore:

`180\cdot(16-2)=180\cdot14=2520`

Therefore, to know how much an interior angle measures, we must divide by the number of angles, that is, 16, like this:

`(2520)/(16)=157.5\text{\degree}`

That is, the measure of one interior angle in a regular 16-gon is 157.5°