How many sides does a polygon have if the sum of its interior angles is 180 degrees?
The formula for the sum of interior angles of any polygon = (n-2)180 degrees. (where n = number of sides of the polygon). Therefore, the polygon has three sides and this implies it is a triangle.
What angles that sum to 180 degrees?
Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees.
Can a polygon have 180 degree angle?
A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive.
Which polygon has an interior angle sum of 1080?
The polygon with an interior angle sum of 1080° is an octagon, or a polygon with 8 sides.
Why is exterior angles always sum to 360?
The sum of the exterior angles of any polygon (remember only convex polygons are being discussed here) is 360 degrees. Because the exterior angles are supplementary to the interior angles, they measure, 130, 110, and 120 degrees, respectively. Summed, the exterior angles equal 360 degreEs.
What is the sum of all interior angles of a 20 sided polygon?
When you divide a polygon into triangles, the number of triangles is always 2 less than the number of sides. This means that all of the interior angles of any 20-sided polygon add up to 3240°.
What is the sum of all interior angles of a 16 sided polygon?
Hence sum of interior angles of a convex 16-sided polygon would be 180∘×(16−2)=180∘×14=2520∘ .
What is the total number of angles in a polygon?
For any polygon, the total degrees in the interior angles equals 180 ( n − 2). A three-sided polygon has 180 degrees. A four-sided one has 360. Five sides gives 540. Etc. So why is it that lim n → inf 180 ( n − 2) = 360? That is, why does a circle, an infinite-sided polygon, have the same number of degrees as a four-sided polygon?
Is the sum of all interior angles always equal to 180 degrees?
But the angle of the sum of all the types of interior angles is always equal to 180 degrees. For a regular triangle, each interior angle will be equal to: 180/3 = 60 degrees
How to find the sum of the interior angles of a polygon?
Sum of Interior Angles of a Polygon. The Sum of interior angles of a polygon is always a constant value. If the polygon is regular or irregular, the sum of its interior angles remains the same. Therefore, the sum of the interior angles of the polygon is given by the formula: Sum of the Interior Angles of a Polygon = 180 (n-2) degrees
How is the exterior angle of a polygon made?
An exterior angle of a polygon is made by extending only one of its sides, in the outward direction. The angle next to an interior angle, formed by extending the side of the polygon, is the exterior angle. Hence, we can say, if a polygon is convex, then the sum of the degree measures of the exterior angles, one at each vertex, is 360°.