Question

the angle sum of a convex polygon with number of sides n is ​

Answer 1

Answer:

360°

Step-by-step explanation:

The exterior angle sum theorem states that the sum of the exterior angles of a convex polygon is 360°. If a convex polygon is regular with “n” number of sides, then each exterior angle of a convex polygon is measured as 360°/n.

• The angle sum of a convex polygon with n sides is given by the formula A = 180 (n − 2)°.
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Answer 2

Given : convex polygon with number of sides n

To Find :   Sum of angles

Solution:

In a convex polygon, any two interior points can be connected with a segment completely inside the polygon.

No line containing a side of a convex polygon passes through the inside of that polygon.

convex polygon with number of sides n  

Hence n exterior angle

interior angle + exterior angle = 180°  ( Linear pair)

Sum of all Interior angles + sum of all exterior angles = n * 180°

sum of all exterior angles = 360°

=> Sum of all Interior angles +   360° = n * 180°

=> Sum of all Interior angles = n * 180° -  360°

=> Sum of all Interior angles = 180° ( n - 2)

=>  Sum of all Interior angles =  ( n - 2)180°

The angle sum of a convex polygon with number of sides n is  ( n - 2)180°

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