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.
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?
- 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?
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.