QuestionFind the number of sides in a regular polygon where the ratio of interior angle to exterior angle is .
Studdy Solution
STEP 1
Assumptions1. The ratio of the interior angle to the exterior angle of the polygon is71.
. The sum of the interior angle and the exterior angle of a polygon is always180 degrees.
3. The sum of all exterior angles of a regular polygon is always360 degrees.
STEP 2
First, we need to find the value of the interior and exterior angles. We can do this by setting up an equation using the given ratio and the fact that the sum of the interior and exterior angles is180 degrees.
Let the common ratio be . Then the interior angle is and the exterior angle is .
STEP 3
Now, plug in the values for the interior and exterior angles to set up the equation.
STEP 4
Combine like terms.
STEP 5
olve for .
STEP 6
Calculate the value of .
STEP 7
Now that we have the value of , we can find the value of the exterior angle, which is .
STEP 8
We know that the sum of all exterior angles of a regular polygon is360 degrees. So, we can find the number of sides of the polygon by dividing360 by the exterior angle.
STEP 9
Plug in the values for the sum of all exterior angles and the exterior angle to calculate the number of sides.
STEP 10
Calculate the number of sides of the polygon.
The polygon has16 sides.
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