Question

What can you say about the angle sum of a convex polygon with a number of sides \[n\] ?
A. \[7\]
B. \[8\]
C. \[10\]
D.none

Answer 1

Hint: To solve these types of questions we need to know the basic theorems which are related to the convex polygon. Also, we need to know how to find the sum of interior angles and the sum of exterior angles to solve these types of questions and to make easy calculations. Also, we need to know the definition of a convex polygon.

Complete step by step solution:
In this question, we would explain how to find the sum of a convex polygon with several sides \[n\] .
Let’s know the definition of a convex polygon,
If the planar polygon contains all the line segments connecting any pair of its points is known as a convex polygon, otherwise, the polygon is known as a concave polygon.
In this problem the convex polygon has \[n\] sides. We know that every convex polygon has two types of angles which are interior and exterior. According to the Theorem if a convex polygon has \[n\] sides, then its interior angle sum is given by the following equation,
 \[S = \left( {n - 2} \right) \times {180^ \circ }\]
Here \[n\] is the number of sides of the convex polygon.
So, the final answer is,
The angle sum of a convex polygon with \[n\] sides can be calculated by \[S = \left( {n - 2} \right) \times {180^ \circ }\] .
So, options \[D)\] none is the correct answer.
So, the correct answer is “Option D”.

Note: To solve these types of questions remember the basic theorems related to the polygon. Also, note that the formula mentioned in the above calculations. Also, note that if we have the polygon with seven sides we would substitute \[7\] instead of \[n\] in the formula \[S = \left( {n - 2} \right) \times {180^ \circ }\] to find the angle sum of a convex polygon with seven sides.