# If all the angles of a hexagon are equal. Find the measure of each of its angles.

A.${100^ \circ }$

B.${240^ \circ }$

C.${140^ \circ }$

D.${120^ \circ }$

Answer

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Hint: Use the information, the sum of interior angles of a polygon $ = {180^ \circ }(n - 2)$.

We have given that all the angles of a hexagon are equal. Let each angle be $x$. We know that the number of sides in a hexagon is 6. Also, the sum of interior angles of a polygon $ = {180^ \circ }(n - 2)$. Using all this information,

$

\Rightarrow 6x = {180^ \circ }(n - 2) \\

\Rightarrow x = {30^ \circ }(6 - 2) \\

\Rightarrow x = {120^ \circ } \\

$

Hence, each angle of the hexagon is ${120^ \circ }$. So, option D is the correct option.

Note: Instead of hexagon, it could be any polygon. Determine the number of sides which is mostly evident from the name of the polygon like in this case it is a hexagon and ‘hex’ implies ‘6’. Use that as $n$ and determine the angles.

We have given that all the angles of a hexagon are equal. Let each angle be $x$. We know that the number of sides in a hexagon is 6. Also, the sum of interior angles of a polygon $ = {180^ \circ }(n - 2)$. Using all this information,

$

\Rightarrow 6x = {180^ \circ }(n - 2) \\

\Rightarrow x = {30^ \circ }(6 - 2) \\

\Rightarrow x = {120^ \circ } \\

$

Hence, each angle of the hexagon is ${120^ \circ }$. So, option D is the correct option.

Note: Instead of hexagon, it could be any polygon. Determine the number of sides which is mostly evident from the name of the polygon like in this case it is a hexagon and ‘hex’ implies ‘6’. Use that as $n$ and determine the angles.

Last updated date: 02nd Oct 2023

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