Question

What is the sum of interior angles of a hendecagon?

Answer 1

Hint: In the above question, we are given a polygon which is a hendecagon. A hendecagon has 11 sides and it almost looks like a circle but it is not round.We have to find the sum of interior angles of a hendecagon. There is a formula to find the sum of interior angles of a polygon. The sum of interior angles of a polygon is given by \[180^\circ \left( {n - 2} \right)\] ,where \[n \geqslant 3\] is the number of sides of a polygon.

Complete step by step answer:
A hendecagon is shown in the below diagram.

We are given a polygon, hendecagon. We have to find the sum of interior angles of the hendecagon. We can find the sum of interior angles of the polygon hendecagon using the formula of sum of interior angles of a polygon. The formula of the sum of interior angles of a polygon is given by \[180^\circ \left( {n - 2} \right)\] where \[n \geqslant 3\]. Since we know that the hendecagon has 11 sides. Therefore, for a hendecagon,
\[ \Rightarrow n = 11\]

Now putting the value of \[n = 11\] in the above formula \[180^\circ \left( {n - 2} \right)\] , we can find the required sum of interior angles of the hendecagon.Therefore, the sum of interior angles of a hendecagon is given by,
\[ \Rightarrow 180^\circ \left( {n - 2} \right)\]
Putting \[n = 11\] in above formula, we get
\[ \Rightarrow 180^\circ \left( {11 - 2} \right)\]
Solving above sum gives,
\[ \Rightarrow 180^\circ \left( 9 \right)\]
Or we can write,
\[ \Rightarrow 180^\circ \times 9\]
Therefore, we get \[ 1620^\circ \].
That is the required sum of interior angles of a hendecagon.

Therefore, the sum of all interior angles of a hendecagon is \[1620^\circ \].

Note: By further calculation, we can also find the value of each interior angle if we know the number of sides of the polygon and the sum of all interior angles of that polygon.Here, the polygon is a hendecagon. So, the number of sides is 11.Therefore, \[n = 11\]. Also, we have found that the sum of all interior angles of a hendecagon is \[1620^\circ \]. So, we can find the value of each interior angle of the hendecagon by dividing the sum of all interior angles by the number of sides of the hendecagon.Therefore, the value of each interior angle of a hendecagon is given by,
\[ \Rightarrow \dfrac{{1620^\circ }}{{11}}\]
On solving, that gives us
\[ \Rightarrow 147.27^\circ \]
Therefore the value of each interior angle of a hendecagon is \[147.27^\circ \] .