Table of Contents
- 1 For which polygon exterior angle is equal to interior angle?
- 2 How many sides has a polygon if the exterior angle of a polygon is one third of the interior angle?
- 3 How do you find the interior and exterior angles of a polygon?
- 4 What are the interior and exterior angles of a pentagon?
- 5 How do you find the exterior angle of a regular polygon?
- 6 What is the measure of the interior angles of this polygon?
For which polygon exterior angle is equal to interior angle?
Polygon Exterior Angle Sum Theorem If a polygon is a convex polygon, then the sum of its exterior angles (one at each vertex) is equal to 360 degrees. Let us prove this theorem: Proof: Consider a polygon with n number of sides or an n-gon.
How many sides has a polygon if the exterior angle of a polygon is one third of the interior angle?
∴ the regular polygon has 8 sides.
How many sides does a regular polygon have if the ratio of an exterior angle to its adjacent interior angle is 1 5?
Polygon has 12 sides – it is dodecagon.
What is the number of sides in a regular polygon if each interior angle is equal to its exterior angle * 1 point?
The number of sides of the regular polygon is 4.
How do you find the interior and exterior angles of a polygon?
The formula for calculating the size of an interior angle is: interior angle of a polygon = sum of interior angles ÷ number of sides. The sum of exterior angles of a polygon is 360°. The formula for calculating the size of an exterior angle is: exterior angle of a polygon = 360 ÷ number of sides.
What are the interior and exterior angles of a pentagon?
The General Rule
| Shape | Sides | Sum of Interior Angles |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
How do you find the number of sides of an exterior angle?
Divide 360 by the amount of the exterior angle to also find the number of sides of the polygon. For example, if the measurement of the exterior angle is 60 degrees, then dividing 360 by 60 yields 6. Six is the number of sides that the polygon has.
What is the number of sides of a regular polygon whose each exterior angle has a measure of 45?
As each exterior angle is 45o , number of angles or sides of the polygon is 360o45o=8 .
How do you find the exterior angle of a regular polygon?
Exterior angle = 180°-144° Therefore, the exterior angle is 36° The formula to find the number of sides of a regular polygon is as follows: Number of Sides of a Regular Polygon = 360° / Magnitude of each exterior angle
What is the measure of the interior angles of this polygon?
What we are given is that there is a regular polygon with exterior angles that equal 120 degrees. Any exterior angle added to its interior angle is equal to 180 degrees because they make a straight angle. Knowing this, we can calculate the measure of the interior angles: The measure of the interior angles of this polygon is 60 degrees.
How to find the number of sides of a regular polygon?
Therefore, the exterior angle is 36° The formula to find the number of sides of a regular polygon is as follows: Number of Sides of a Regular Polygon = 360° / Magnitude of each exterior angle Therefore, the number of sides = 360° / 36° = 10 sides
Why is a regular polygon an equilateral triangle?
Solution: Since the polygon is regular, the measure of all the interior angles is the same. Therefore, all its exterior angles measure the same as well, that is, 120 degrees. Since the polygon has 3 exterior angles, it has 3 sides. Hence it is an equilateral triangle.