Question

How many right angles are in a regular pentagon?

Answer 1

Hint: To find whether in a regular pentagon, there are right angles or not. First we should know about the right angle, which is of $ {90^\circ } $ . Then, with the help of formulae to find the interior angle of a regular pentagon, we will find the interior angle.

Complete step-by-step answer:
There are no right angles among interior angles of a regular pentagon.
Now,
We can find the regular $ N - sided $ polygon has interior angle equal to:
(We have the formula to find the interior angle of a regular pentagon.)
 $ \Phi = {180^\circ }.\dfrac{{N - 2}}{N}(degrees) $
As we know, Pentagon has 5 sides or In case of a regular 5-sided polygon (pentagon) the interior angles measure at:
 $ \phi = {180^\circ }.\dfrac{{5 - 2}}{5} = {108^\circ } $

Therefore, each interior angle of a regular pentagon has $ {108^\circ } $ .
Hence, there is not any right angle among interior angles of a regular pentagon.
So, the correct answer is “O”.

Note: If the interior angle of a pentagon is not equal to $ {108^\circ } $ , then it is said to be irregular pentagon. As in a regular pentagon, the exterior angle is equal to $ {72^\circ } $ each. And, if all the vertices of a pentagon lie on the circumference of a circle, then it is called a cyclic pentagon.