How do you find angles in a polygon?
Emma Martin
Updated on April 28, 2026
A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.
.
Also to know is, what are the angles of a polygon?
The General Rule
| Shape | Sides | Sum of Interior Angles |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
Similarly, is circle a polygon? Polygons. A polygon is a closed plane figure with three or more sides that are all straight. The following figure is not a polygon as it is not a closed figure. A circle is not a polygon as it does not have straight sides.
Besides, how many angles does a polygon have?
A polygon has as many angles as it has sides. For example, a triangle has 3 sides and 3 angles. A pentagon has 5 sides and 5 angles. An octadecagon has 18 sides and 18 angles!
What is the formula for finding interior angles of a polygon?
An interior angle is located within the boundary of a polygon. The sum of all of the interior angles can be found using the formula S = (n - 2)*180. It is also possible to calculate the measure of each angle if the polygon is regular by dividing the sum by the number of sides.
Related Question AnswersWhat is the exterior angle of a pentagon?
How is the exterior angle of a regular pentagon calculated? The sum of the exterior angle of all polygon is equal to 360deg.How do you find the exterior angles of a polygon?
To find the value of a given exterior angle of a regular polygon, simply divide 360 by the number of sides or angles that the polygon has. For example, an eight-sided regular polygon, an octagon, has exterior angles that are 45 degrees each, because 360/8 = 45.What is the interior and exterior of an angle?
In summary, we learned that an interior angle is an angle inside a shape, while an exterior angle is an angle made by the side of a shape and a line drawn out from an adjacent side. The sum of the interior angles of a triangle is always 180.Why do the exterior angles of a polygon equal 360?
The sum is always 360 . Geometric proof: When all of the angles of a convex polygon converge, or pushed together, they form one angle called a perigon angle, which measures 360 degrees. If the sides of the convex polygon are increased or decreased, the sum of all of the exterior angle is still 360 degrees.Is a triangle a regular polygon?
A regular polygon is a polygon where all of the sides and angles are the same. An equilateral triangle is a regular polygon. It has all the same sides and the same angles. An isosceles triangle has two equal sides and two equal angles.How many sides does a polygon have if the sum of its interior angles is 720?
6 sidesWhat is another name for a polygon?
Names of Polygons| Name | Sides | Interior Angle |
|---|---|---|
| Heptagon (or Septagon) | 7 | 128.571° |
| Octagon | 8 | 135° |
| Nonagon (or Enneagon) | 9 | 140° |
| Decagon | 10 | 144° |
How many sides does a regular polygon have if the interior angle is 165?
24 sidesWhat is the sum of interior angles in a polygon?
The sum of the measures of the interior angles of a polygon with n sides is (n – 2)180. If you count one exterior angle at each vertex, the sum of the measures of the exterior angles of a polygon is always 360°.What are the 12 kinds of polygons?
Types of Polygons- Regular Polygons. They have equal angles and sides.
- Irregular Polygons. They do not have equal angles and sides. Types of Polygons based on Number of Sides.
- Triangle. 3 sides.
- Quadrilateral. 4 sides.
- Pentagon. 5 sides.
- Hexagon. 6 sides.
- Heptagon. 7 sides.
- Octagon. 8 sides.
