## How do you prove that the sum of the exterior angles of a polygon is 360 degrees?

1 Expert Answer The sum of the interior angles of a regular polygon with n sides is 180(n-2). So, each interior angle has measure 180(n-2) / n. Each exterior angle is the supplement to an interior angle. Sum of exterior angles = n(360 / n) = 360.

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### Why do the exterior angles of a triangle add up to 360 degrees?

We also know that in a triangle, the interior angle and its corresponding exterior angle form a linear pair, i.e., Exterior angle = 180° – Interior angle. Hence, the sum of exterior angles of an equilateral triangle is equal to 360 degrees.

**What do the exterior angles of a polygon always add up to?**

Sal demonstrates how the the sum of the exterior angles of a convex polygon is 360 degrees.

**Do angles in a polygon add up to 360?**

The sum of the exterior angles of a polygon is 360°.

## Do all polygons interior angles add up to 360?

The common property for all the above four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees.

### How do you prove exterior angles of a triangle equal 360?

Expert Answer:

- Let x, y and z be the exterior angles of a triangle.
- Then the corresponding interior angles are:
- 180o – x, 180o – y, 180o – z.
- Since the sum of interior angles is 180o, therefore.
- 180o – x + 180o – y + 180o – z = 180o
- Or, 540o – (x + y + z) = 180o
- Or, x + y + z = 540o – 180o = 360o.

**Is the sum of the exterior angles 360 degrees in every hexagon?**

By the sum of exterior angles formula, Each exterior angle of a regular polygon of n sides = 360° / n. Answer: Each exterior angle of a regular hexagon = 60°. Example 2: Use the sum of exterior angles formula to prove that each interior angle and its corresponding exterior angle in any polygon are supplementary.

**What are angles that add up to 360 degrees called?**

Answer and Explanation: When the sum of the measures of two angles is 360°, we call the two angles explementary angles.

## Do the angles of a Pentagon add up to 360?

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°.

### Do exterior angles add up to 180?

An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.

**What is a 360 degree polygon?**

Quadrilaterals (Squares, etc) The interior angles in a triangle add up to 180° … and for the square they add up to 360° … because the square can be made from two triangles!

**What do the exterior angles of a Pentagon add up to?**

360°

Sum of Exterior Angles in a Pentagon Therefore, the sum of exterior angles of a polygon = n(360°/n). As, the number of sides in a pentagon is 5, n=5. Thus, the sum of exterior angles of a pentagon = 5(360°/5) = 360°.

## What do the exterior angles of a triangle add up to?

The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than either of the opposite interior angles. The exterior angle and the adjacent interior angle are supplementary. All the exterior angles of a triangle sum up to 360º.

### What is the sum of the measures of the exterior angles of a polygon that has fifteen sides?

What is the sum of the exterior angles in a regular 15-gon? The sum of the exterior angles in any convex polygon, including a regular 15-gon, is 360∘.

**What is the exterior angle of a polygon?**

An exterior angle of a polygon is an angle at a vertex of the polygon, outside the polygon, formed by one side and the extension of an adjacent side. Notice that corresponding interior and exterior angles are supplementary (add to 180°).

**Why is it called 360 degrees?**

And they then made a leap and decided to divide this circle on the sky—and all circles—into 360 even parts so that the Sun would move through 1 part per day. Each of these parts was dubbed 1 degree, thus giving us the idea that a circle contains 360 degrees.