Question

The sum of interior angles in a 14-gon is how many degrees?

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

Complete step by step answer:
The given polygon is a 14-gon. The number of sides in a polygon is fourteen.
So, to find the sum of angles, we just put the value into the formula of sum of angles,
Sum of angles \[= {\rm{ }}\left( {n - 2} \right) \times 180\]
Hence, sum of angles of polygon \[ = \left( {14 - 2} \right) \times 180 = 12 \times 180 = 2160^\circ \]

Thus, the sum of interior angle measures in polygon is \[2160^\circ \].

Note: In the given question, we had to find the sum of the measures of all the interior angles in a polygon. We solved this question by putting in the value into the formula for this question. Here, the number of sides was given. But, a lot of students make mistakes when the number of sides is not given, rather the name of the figure is given. They get confused for the number of sides of the given figure, put in incorrect value and calculate the wrong answer. So, we must remember the number of sides of all the standard figures.