Question

What is the measure of each interior angle of an 18-sided polygon?

Answer 1

Hint: Here the given question is about to find the sum of all interior angles of an 18-sided polygon. We will use the formula to find the interior angles of the polygon. We need to substitute 18 in the formula to get the value of the sum of interior angles of the polygon. Then for the measure of each interior angle, we will divide the sum of interior angles by 18.

Complete step-by-step solution:
The formula for finding the interior angles is \[\left( n-2 \right)\times {{180}^{\circ }}\], here n is the number of sides of the polygon.
Here is the diagram of 18-sided polygon,

We know that a polygon has 18 sides. Then the value of n is 18.
Now we will use the formula of sum of interior angles of a polygon to find out the sum.
Substituting the value of number of sides in the formula \[\left( n-2 \right)\times {{180}^{\circ }}\], we get
Sum of interior angles \[=\left( 18-2 \right)\times {{180}^{\circ }}\]
On further simplification,
\[\begin{align}
  & =16\times {{180}^{\circ }} \\
 & ={{2880}^{\circ }} \\
\end{align}\]
The sum of interior angles is \[{{2880}^{\circ }}\].
For finding the measure of each interior angle of an 18-sided polygon, we need to divide the sum of interior angles by the number of sides of the polygon.
Measure of each interior angle\[=\dfrac{{{2880}^{\circ }}}{18}={{160}^{\circ }}\].
Hence, the measure of each angle is \[{{160}^{\circ }}\].

Note: A polygon is defined as a two-dimensional figure or a plane figure, which is represented by a finite number of straight lines which are connected to form a closed form. We must know about the sum of the interior angles of the basic polygons as
TRIANGLE has the sum of the interior angles is \[{{180}^{\circ }}\].
PENTAGON has the sum of the interior angles is \[{{360}^{\circ }}\].