Question

The sum of all angles of a quadrilateral is:
(A) \[{180^ \circ }\]
(B) \[{270^ \circ }\]
(C) \[{360^ \circ }\]
(D) \[{400^ \circ }\]

Answer 1

Hint: In the given question, we are asked to find the sum of angles of a quadrilateral. So, we know the angle sum formula for polygons. So, we can substitute the number of sides of a polygon into the formula so as to get the angle sum of that polygon. The question revolves around the basic properties of different kinds of polygons.

Complete step by step solution:
In the given question, we have to find the angle sum of a quadrilateral.
Quadrilateral is a two dimensional closed figure with four sides, four vertices and four angles.
Now, we know that there is a formula to find the angle sum of a polygon.
So, the formula for finding the angle sum of a n sided polygon is $\left( {n - 2} \right){180^ \circ }$.
So, for finding the angle sum of a quadrilateral, we substitute the value of n as $4$ since there are $4$ sides in a quadrilateral. So, we get the angle sum of a quadrilateral as,
$ \Rightarrow \left( {4 - 2} \right){180^ \circ }$
$ \Rightarrow \left( 2 \right) \times {180^ \circ }$
$ \Rightarrow {360^ \circ }$
Hence, the angle sum of a quadrilateral is ${360^ \circ }$. So, option (C) is correct.

Note:
In the given question, the result obtained should be learnt by heart and can be used as a basic result in other complex questions and problems. One should know the formula to find the angle sum of a polygon so as to attempt the given problem. One must also take care of the calculation while doing such a question so as to be careful of the final answer.