Question

Three angles of a seven sided polygon are ${132^ \circ }$ each and the remaining four angles are equal. Find the value of each equal angle.
$
  A){126^ \circ } \\
  B){116^ \circ } \\
  C){120^ \circ } \\
  D){146^ \circ } \\
 $

Answer 1

Hint- Here in this question first we will apply the formula of sum of interior angles of a polygon i.e. $\left( {2n - 4} \right){90^ \circ }$ then we apply the conditions given in the question.
Complete step-by-step answer:

Here, given that the polygon is a seven sided and three angles of which are ${132^ \circ }$each
Also it is given that the remaining four angles are equal.
Now we have to find the value of each equal angle.
We know that,
The sum of interior angles of a n sided polygon $ = \left( {2n - 4} \right){90^ \circ }$ where n is the number of sides.
And for this polygon, n=7
Now, sum of interior angles $ = \left( {2 \times 7 - 4} \right){90^ \circ }$
$ = \left( {14 - 4} \right){90^ \circ }$
Or sum of interior angles$ = {900^ \circ }$
Also it is given that three angles are each ${132^ \circ }$
$ \Rightarrow $ 3 angles $ = 3 \times {132^ \circ } = {396^ \circ }$
Thus, the remaining 4 angles $ = {900^ \circ } - {396^ \circ }$
$ = {504^ \circ }$
Also it is given in the question that the remaining four angles are equal.
Thus, each of the 4 angles $ = \dfrac{{{{504}^ \circ }}}{4}$
$ = {126^ \circ }$
Thus, the correct option is (A).
Note- In order to solve this question one must know the concept of polygon. A polygon is any 2-Dimensional closed shape formed with straight lines. It is of two types i.e. regular and irregular polygon.