Question

Two angles of an eight sided polygon are \[{{142}^{\circ }}\] and \[{{176}^{\circ }}\]. If the remaining angles are equal to each other; find the magnitude of each of the equal angles.
A. \[{{127}^{\circ }}\]
B. \[{{107}^{\circ }}\]
C. \[{{120}^{\circ }}\]
D. \[{{140}^{\circ }}\]

Answer 1

Hint:In the above question we will have to know about the sum of interior angles of a polygon of ‘n’ sides which is given as bellows:Sum of interior angles \[=\left( n-2 \right)\times {{180}^{\circ }}\].They given two angles of eight sided polygon.Let us consider remaining angles to be ‘a’ and using this formula find the required answer.

Complete step-by-step answer:
We have been given the two angles of an eight sided polygon are \[{{142}^{\circ }}\] and \[{{176}^{\circ }}\].
Also, we know that a polygon of ‘n’ sides form n interior angles.
So, in a polygon of eight sides there are a total 8 interior angles.
Let us suppose the remaining six angles to be ‘a’ of the given polygon.
Sum of interior angles \[=\left( 8-2 \right)\times {{180}^{\circ }}={{1080}^{\circ }}\].
\[=142+176+a+a+a+a+a+a=1080\]
On solving the above equation, we get,
\[318+6a=1080\]
On subtracting 318 both sides of equality, we get,
\[\begin{align}
  & 6a=1080-318 \\
 & 6a=762 \\
\end{align}\]
On dividing the equation by 6, we get,
\[\begin{align}
  & a=\frac{762}{6} \\
 & \Rightarrow a={{127}^{\circ }} \\
\end{align}\]
Hence the magnitude of each angle is ${{127}^{\circ }}$.
Therefore, the correct option of the above question is option A.

Note: Students should remember the formula related to the polygons like the sum of the interior angles and the number of angles formed by a polygon of ‘n’ sides i.e\[=\left( n-2 \right)\times {{180}^{\circ }}\].