Question

How do you find the measure of each interior angle of a polygon?

Answer 1

Hint:
In the given question, we have been given to ask the measure of each angle of a regular polygon. To solve this question, first, we need to know the meaning of the polygon in question – the number of sides of the polygon. Since we have no information as of the given question, we are going to consider two cases – we are given the polygon, or, we are given the total sum of angles.

Formula Used:
When the number of sides of a polygon is \[n\], then the total sum of all the angles is
\[sum = \left( {n - 2} \right) \times 180\]

Complete step by step answer:
For solving this question, we are going to consider two cases:
We are given the name of the polygon.
Here we know the name of the polygon, hence we know the number of sides it has.
Let the number of sides be \[n\].
When we have been given the number of sides, we just put in this formula:
\[angle = \dfrac{{\left( {n - 2} \right) \times 180}}{n}\]
We are given the total sum of the angles.
Here we know the total sum of angles. Let it be \[A\].
In this case, we put in this formula to first find the number of sides:
\[A = \left( {n - 2} \right) \times 180\]
Then, when we evaluate \[n\], we put in the formula in the first case and evaluate the answer.

Note:
In the given question, we had been asked how we could find the measure of each angle of a polygon – it has to be a regular polygon only, as we cannot say what the measure of any angle is. Then we considered the two cases and found the value of the required thing using different formulas for each case.