Question

How do you find the sum of interior angle measures in a hexagon?

Answer 1

Hint:
In the given question, we have to find the sum of the measures of all the interior angles in the given polygon. To do that, we only needed to know the meaning of the prefix word “hexa” – the number of sides it represents. Then we just put this number into the formula of the sum of angles of a polygon. And that gives us the answer.

Formula Used:
In this question, we are going to use the formula of sum of angles of a polygon with \[n\] sides:
\[sum{\text{ }}of{\text{ }}angles{\text{ }} = {\text{ }}\left( {n - 2} \right) \times 180\]

Complete step by step answer:
The given polygon is a hexagon. The number of sides in a hexagon is \[6\].
So, to find the sum of angles, we just put the value into the formula of sum of angles,
\[sum{\text{ }}of{\text{ }}angles{\text{ }} = {\text{ }}\left( {n - 2} \right) \times 180\]
Hence, sum of angles of hexagon \[ = \left( {6 - 2} \right) \times 180 = 4 \times 180 = 720^\circ \]

Thus, the sum of interior angle measures in the hexagon is \[720^\circ \].

Note:
In the given question, we had to find the sum of the measures of all the interior angles in a hexagon. To do that, we only needed to know the meaning of the word “hexa” – six; we have to find the measure of the sum of interior angles of a figure with six sides. Then we just put the number of sides into the formula of the sum of angles of a polygon, and that gave us the answer.