Question

A convex polygon has 7 sides, and each vertex has one angle. What is the sum of the measures of its exterior angles?

A) 360 degrees
B) 450 degrees
C) 540 degrees
D) 630 degrees
E) 720 degrees

Answer 1

The sum of the exterior angles of any convex polygon, including one with 7 sides, is always 360 degrees.

Step-by-step explanation:

The sum of the measures of the exterior angles of any polygon, whether it's a triangle, a pentagon or a heptagon, is always 360 degrees. This is true regardless of the number of sides in the polygon.

To illustrate, imagine walking around the polygon, turning at each vertex to continue to the next side. The sum of all the turns you make will always add up to one full revolution, which is 360 degrees. This rule can be used for any convex polygon, including the seven-sided polygon mentioned in the question.