Interior and Exterior Angle of a Polygon: Formula not working

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Homework Help Overview

The problem involves determining the number of sides in a polygon based on the relationship between its interior and exterior angles, specifically when each interior angle is stated to be 8 times the measure of each exterior angle.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the setup of the equations for interior and exterior angles and attempt to solve for the number of sides, n. Some participants question the calculations and suggest simplifying the equations earlier in the process.

Discussion Status

There is an ongoing examination of the calculations involved in solving the problem. One participant identifies a mistake in their earlier work, leading to a revised conclusion about the number of sides in the polygon. However, there is no explicit consensus on the final answer as the discussion continues to explore the reasoning behind the calculations.

Contextual Notes

Participants are working under the constraints of homework rules that require them to show their reasoning and calculations without providing direct solutions. There is a focus on identifying and correcting errors in the mathematical process.

zak100
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Homework Statement


How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?

Homework Equations


Interior angle of a polygon: ((n-2) * 180)/n
Exterior angle of a polygon: (360)/n

The Attempt at a Solution


((n-2) * 180)/n = 8 * (360)/n
now ((n-2) * 180) = 8 * 360
180 n -360 = 8 * 360
180 n = 7 * 360
n = 14
I am getting n = 14 which is wrong.

Some body please guide me what is the problem.

Zulfi.
 
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zak100 said:

Homework Statement


How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?

Homework Equations


Interior angle of a polygon: ((n-2) * 180)/n
Exterior angle of a polygon: (360)/n

The Attempt at a Solution


((n-2) * 180)/n = 8 * (360)/n
now ((n-2) * 180) = 8 * 360
180 n -360 = 8 * 360
Work is fine to here, but you have a mistake in the line below. Two lines above, it would be simpler to divide both sides by 180, to get simpler numbers to work with.
Alternatively, in the line above, you are adding 360 to both sides of the equation.
zak100 said:
180 n = 7 * 360
n = 14
I am getting n = 14 which is wrong.

Some body please guide me what is the problem.

Zulfi.
 
zak100 said:
180 n -360 = 8 * 360
180 n = 7 * 360

Check the math

EDIT: beaten for some seconds by Mark44
 
Last edited:

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