Question

All angles of a regular polygon are
A. $90{}^\circ $
B. $180{}^\circ $
C. $60{}^\circ $
D. equal in measure.

Answer 1

Hint: We should have a basic knowledge that a polygon is a closed figure that is made by joining three or more straight lines and a regular polygon is a polygon that is equilateral. We can find the angles of a regular polygon by using the formula, $\dfrac{\text{sum of interior angles}}{\text{number of sides}}$.

Complete step by step solution:
We have been asked in the question to find the measure of all the angles in a regular polygon. Now, before we start solving, we should know what a regular polygon and a polygon are. A polygon is a 2-dimensional closed figure which is formed by joining three or more straight lines. For example,

Now, a regular polygon is a polygon that is equilateral, that is, which has all the sides of the same length. Now, we have the formula for finding the angles of the regular polygon, which is given as,
$\dfrac{\text{sum of interior angles}}{\text{number of sides}}\ldots \ldots \ldots \left( i \right)$
Now, we know that the formula for calculating the sum of the interior angles is given as,
$\left( n-2 \right)\times 180{}^\circ \ldots \ldots \ldots \left( ii \right)$
Where n is the total sides of the regular polygon. So, using equations (i) and (ii), we can say that all the angles of the regular polygon are given by,
$\dfrac{\left( n-2 \right)\times 180{}^\circ }{n}$
So, we can see that all angles of a regular polygon are equal in measure.
Therefore, the correct answer is option D.

Note: The students might look at the options and use them, like they may think that option A as correct as they might think that rectangle is a polygon and all the angles of a rectangle are $90{}^\circ $. They may also think of an equilateral triangle, where all the angles are $60{}^\circ $ and take option C as the correct answer.