# What Is The Exterior Angle Sum Of A Convex Pentagon?

Polygon Exterior Angle Sum Theorem. If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° .

If the sides of the convex polygon are increased or decreased, the sum of all of the exterior angle is still 360 degrees. Beside this, what is the exterior angle of a pentagon? The sum of the exterior angle of all polygon is equal to 360deg. What is the formula for finding exterior angles of a polygon?

## Interior Angles in Convex Polygons: Lesson (Geometry Concepts)

### What is the sum of a convex pentagon?

How? Since these 5 angles form a perfect circle around the point we selected, we know they sum up to 360°. So, the sum of the interior angles in the simple convex pentagon is 5*180°-360°=900°-360° = 540°. It is easy to see that we can do this for any simple convex polygon.

### What is the formula in finding the sum of the exterior angles of a convex polygon?

Theorem 39: If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = ( n −2) × 180°. ... Example 2: Find the exterior angle sums, one exterior angle at each vertex, of a convex nonagon. The sum of the exterior angles of any convex polygon is 360°.

### What is the measure of each exterior angle in a regular convex pentagon?

360∘nIf the polygon is regular with n sides, this means that each exterior angle is 360∘n.

### What is the sum of the exterior angle measures?

Since, we are required the sum, it's simply 360∘. If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360∘. To find the measure of each exterior angle of a regular polygon, you just divide 360∘ degrees by the number of sides.

### What is the measure of the central angle of a pentagon?

The measure of central angle a regular pentagon makes a circle, i.e. total measure is 360°. If we divide pentagon into five congruent triangles, then the angle at one vertex of them will be 72° (360°/5 = 72°).