Interior angles of a regular polygon

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SUMMARY

The discussion focuses on determining the number of sides of two regular polygons with a side ratio of 5:4 and a 6-degree difference in their interior angles. The interior angle (α) of a regular polygon can be calculated using the formula α = (n - 2) * 180° / n, where n is the number of sides. By setting up equations based on the given ratio and angle difference, the solution reveals that the polygons have 10 and 8 sides, respectively.

PREREQUISITES
  • Understanding of regular polygon properties
  • Knowledge of interior angle formulas
  • Basic algebra for solving equations
  • Familiarity with geometric concepts involving triangles
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  • Study the formula for calculating interior angles of regular polygons
  • Explore the relationship between central angles and interior angles
  • Practice solving problems involving ratios of polygon sides
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johncena
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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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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.
 
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?
 

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