Question

What is the measure of an interior angle of a 21-gon?162.86°90°360°3420°

Answer 1

Question:

What is the measure of an interior angle of a 21-gon?

Concept:

Define a 21-gon

A 21-gon is a 21 sided polygon also know as An icosikaihenagon

In the case of this polygon, the value of n is

`n=21`

We will then calculate the sum of interior angles of a 21-gon and then divide the sum by the number of sides n...

Therefore,

The formula we will use to calculate the measure of an interior angle of a 21-gon is given below as

`\begin{gathered} \text{meausre of an interior angle=}\frac{\text{sum of interior angles}}{\text{total number of sides}} \\ \end{gathered}`

The formula for the sum of interior angles is given below as

`\text{sum of interior angle=(n}-2)*180`

Hence,

We will have

`\begin{gathered} \text{meausre of an interior angle=}\frac{\text{sum of interior angles}}{\text{total number of sides}} \\ \text{meausre of an interior angle}=((n-2)*180^0)/(n) \end{gathered}`

Step 2:

Substitute the value of n=21 in the formula above, we will have

`\begin{gathered} \text{measure of an interior angle}=((n-2)*180^0)/(n) \\ \text{measure of an interior angle}=((21-2)*180^0)/(21) \\ \text{measureof an interior angle}=(19*180^0)/(21) \\ \text{measure of an interior angle}=(19*180^0)/(21) \\ \text{measure of an interior angle}=(3420^0)/(21) \\ \text{measure of an interior angle}=162.86^0 \end{gathered}`

Hence,

The final answer = 162.86°