Question

The sum of all the angles of a pentagon are
$
  (a){\text{ 36}}{{\text{0}}^0} \\
  (b){\text{ 54}}{{\text{0}}^0} \\
  (c){\text{ 72}}{{\text{0}}^0} \\
  (d){\text{ none of these}} \\
 $

Answer 1

Hint – In this question use the direct formula that the sum of the interior angles of a polygon is $\left( {n - 2} \right){180^0}$, where n is the total number of sides of a pentagon. The total number of sides will be 5. Use this approach to get the answer.
Complete step-by-step solution -

As we know that the pentagon has 5 sides also shown in the above figure of pentagon.
And we also know that the sum of interior angles of a polygon is =$\left( {n - 2} \right){180^0}$, where n is the number of sides.
So in pentagon n = 5.
Therefore, sum (S) of all the angles in a pentagon = $\left( {5 - 2} \right){180^0}$
$S = 3\left( {{{180}^0}} \right) = {540^0}$
So this is the required answer.
Hence option (B) is correct.

Note – In geometry a pentagon is any five sided polygon. The sum of interior angles of a simple polygon is ${540^0}$. A pentagon may be simple or self-intersecting. A self-intersecting regular polygon is called a pentagram. Angles in such shapes are broadly classified into interior and exterior angles. Interior angle is the angle between the adjacent sides of a rectilinear figure, whereas exterior angle is the angle between any side of a shape and a line extended from the next side.