Interior angles of a regular polygon

In summary, the number of sides of two regular polygons are in a ratio of 5:4 and the difference between their interior angles is 6 degrees. To determine the number of sides, you can draw a triangle with one vertex at the center of the polygon and the other two vertices at consecutive edges. This triangle will have angles that add up to 180 degrees, allowing you to solve for the number of sides. Additionally, the central angle and interior angle of the polygon must have a certain relation in order for this method to work.
  • #1
johncena
131
1
The number of sides of two regular polygons are in the ratio 5:4 and the difference between their interior angles is 6 degrees.Find the number of sides of the two polygons.

I forgot the relation between interior angles and the number of sides of a regular polygon.Can anyone help me to figure out the relation ?
 
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  • #2
Call alpha the interior angle, and draw a triangle having as vertex 2 consecutive vertex of the polygon and the center of the polygon. You know all the angles in this triangle, and they are related by the fact that those 3 angles add up to 180 degrees. Solve for the number of edges of the polygon.
 
  • #3
Hint:
Draw a triangle with one vertex at the polygonal centre, the other two vertices being the end points of a polygonal edge.

a) What relation between the number of sides and the angle associated with the centre vertex must exist?
b) What relation must exist between the central angle and the interior angle of the polygon?
 

1. What is a regular polygon?

A regular polygon is a two-dimensional shape with equal sides and angles. It can have any number of sides, but all of its angles and sides are congruent, or equal in measure.

2. How do I find the interior angle of a regular polygon?

To find the interior angle of a regular polygon, you can use the formula (n-2) x 180 / n, where n is the number of sides. For example, a regular hexagon (6 sides) would have an interior angle of (6-2) x 180 / 6 = 120 degrees.

3. What is the sum of the interior angles of a regular polygon?

The sum of the interior angles of a regular polygon is given by the formula (n-2) x 180, where n is the number of sides. For example, a regular hexagon (6 sides) would have a sum of (6-2) x 180 = 720 degrees.

4. Can the interior angles of a regular polygon be different?

No, the interior angles of a regular polygon are always equal in measure. If any angle were to be different, it would make the shape irregular.

5. How are the interior angles of a regular polygon related to its exterior angles?

The interior and exterior angles of a regular polygon are supplementary, meaning they add up to 180 degrees. This means that if you know one angle, you can easily find the other by subtracting it from 180 degrees.

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