Question

What is the sum of the measures of the interior angles of an octagon?

Answer 1

Hint: In this problem, we have to find the sum of the measures of the interior angles of an octagon. We should know that the general formula to find the sum of the interior angle of any polygon is \[180\left( n-2 \right)\], where n is the number of sides of the polygon. Here we have to find the sum of the measures of the interior angles of an octagon as we know that an octagon has 8 sides. We can now substitute the value of n as 8, to get the final answer.

Complete step-by-step solution:
Here we have to find the sum of the measures of the interior angles of an octagon.
We know that the general formula to find the sum of the interior angle of any polygon is \[180\left( n-2 \right)\], where n is the number of sides of the polygon.
Here we have to find the sum of the measures of the interior angles of an octagon as we know that an octagon has 8 sides.
We can now substitute n = 8 in \[180\left( n-2 \right)\], we get
\[\Rightarrow 180\left( 8-2 \right)\]
We can now simplify the above step, we get
\[\Rightarrow 180\left( 6 \right)={{1080}^{\circ }}\]
Therefore, the sum of the measures of the interior angles of an octagon is \[{{1080}^{\circ }}\].

Note: We should always remember that an octagon has 8 sides. We should also remember that the general formula to find the sum of the interior angle of any polygon is \[180\left( n-1 \right)\], where n is the number of sides of the polygon. We can divide the sum of the interior measures of the angle by the number of sides to get the measure of angle in each side.