Question

What is the sum of the measures of the exterior angles of any convex polygon

Answer 1

 If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360°

Answer 2

Answer:

360 degrees is  sum of the measures of the exterior angles of any convex polygon.

Step-by-step explanation:

Convex Polygon:

• A convex polygon is a polygon with all its interior angle less than 180 degrees.
• Thus, all the vertices of the polygon will be away from the interior of the polygon.
• If all the angles are not less than 180 degrees then it becomes concave polygon.
• Example: Triangle is a convex polygon with three sides.

Exterior angle sum Property:

• If we extend the side of the polygon, then the angle formed by the extended side and polygon side is an exterior angle.
• The sum of all the exterior angles if a convex polygon is 360 degrees.
• If this convex polygon is a regular polygon, then the sum is 360 degrees and each exterior angle is equal to $\frac{360}{n}$, where n is the number of sides in regular polygon.