Question

What are the degrees of a 12 sided-polygon?

Answer 1

Hint: In the above type of question we need to find the angle that is made interior and exterior for this we are first going to use the formula that is \[\dfrac{360}{n}\] where n is the number of sides and after finding the exterior angle we will subtract the value of exterior angle by \[{{180}^{\circ }}\] to find the interior angle.

Complete step by step solution:
In the above mentioned question when the question hasn't specified on which angle we should take out we will be taking out every angle i.e. exterior and interior angles. Interior angle is the angle that is between the two lines of the polygon and the exterior angle is the angle that is between the two lines of polygon but lies outside of the polygon. As the number of sides of a polygon increases the interior angle decreases and the exterior angle increases. Now to calculate the interior angle there is a formula which can be used i.e. \[\dfrac{360}{n}\] in this n is the number of sides of a polygon. By using this we can get the interior angle of the polygon. We will substitute 12 in place of n as the number of sides in a polygon mentioned in the question is 12 and we will get:
\[\begin{align}
  & I=\dfrac{360}{12} \\
 & \Rightarrow I={{30}^{\circ }} \\
\end{align}\]
From this we got the interior angle as \[{{30}^{\circ }}\]. Now to calculate the exterior angle we will subtract the interior angle by \[{{180}^{\circ }}\]as the maximum angle two lines can make is \[{{180}^{\circ }}\].
So we get the exterior angle as:
\[\begin{align}
  & E=180-I \\
 & \Rightarrow E=180-30 \\
 & \Rightarrow E={{150}^{\circ }} \\
\end{align}\]
So we have got both the exterior and the interior angle as \[{{150}^{\circ }}\] and \[{{30}^{\circ }}\] respectively.

Note: In this type of questions when nothing is mentioned particularly try to calculate everything related to the question like in the above question it was mentioned take out the angle of a 12 sided polygon but which angle that was not specified so we calculated both the angles i.e. exterior and interior.