Question

Find the sum of all interior angles of the regular polygon with 11 sides. Also, find the measures of each angle.

Answer 1

Hint: We have to find the sum of the interior angles of the regular polygon with 11 sides. We will use the formula to find the interior angles of the polygon. We will substitute 11 in the formula to get the value of the sum of the interior angles of the polygon. Then for the measure of each interior angle, we will divide the sum of interior angles by 11.

Formula used:
Here we will use the formula \[\left( {n - 2} \right) \times 180^\circ \], here \[n\] is the number of sides of the polygon.

Complete step-by-step answer:
We will first draw the diagram of a polygon with 11 sides.

We know that the polygon has 11 sides. Thus, the value of \[n\] is 11.
Now we will use the formula of sum of interior angles of a polygon to find the sum.
Putting the value of number of sides in the formula \[\left( {n - 2} \right) \times 180^\circ \], we get
Sum of interior angles\[ = \left( {11 - 2} \right) \times 180^\circ \]
On further simplification, we get
Sum of interior angles\[ = 9 \times 180^\circ = 1620^\circ \]
Now, we will find the measure of each angle of a polygon. For that, we will divide the sum of interior angles by the number of sides of the polygon.
Measure of each angle\[ = \dfrac{{1620^\circ }}{{11}} = 147.27^\circ \]
Hence, the measure of each angle is \[147.27^\circ \].

Note: A polygon is defined as a plane figure or two-dimensional figure, which is represented by a finite number of straight lines which are connected to form a closed figure. We need to keep in mind that a polygon having 6 sides is known as a hexagon, a polygon with 5 sides is known as a pentagon, and a polygon with 8 sides is known as octagon.
A circle is not a polygon as a circle doesn’t have straight sides. All types of polygon are a two-dimensional plane figure.