How to find angle measures of the corollary to the Polygon Angle-Sum Theorem
To find the angle measures of the corollary to the Polygon Angle-Sum Theorem, we need to understand the Polygon Angle-Sum Theorem first
To find the angle measures of the corollary to the Polygon Angle-Sum Theorem, we need to understand the Polygon Angle-Sum Theorem first.
The Polygon Angle-Sum Theorem states that the sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees.
The corollary to this theorem states that if a polygon is regular, meaning all sides and angles are congruent, then each interior angle of the polygon can be found by dividing the sum of the interior angles by the number of sides.
So, to find the angle measures of the corollary, we need to know the number of sides of the regular polygon and the sum of the interior angles.
Let’s take an example:
Suppose we have a regular polygon with 6 sides. We can use the Polygon Angle-Sum Theorem to find the sum of the interior angles:
Sum of interior angles = (n-2) * 180
= (6-2) * 180
= 4 * 180
= 720 degrees
Now, to find the measure of each interior angle, we divide the sum of the interior angles by the number of sides:
Measure of each interior angle = Sum of interior angles / Number of sides
= 720 / 6
= 120 degrees
Therefore, each interior angle of the regular polygon with 6 sides measures 120 degrees.
By following the same steps for any regular polygon, you can find the angle measures of the corollary to the Polygon Angle-Sum Theorem. Just plug in the appropriate value for the number of sides and solve for the measure of each interior angle using the formulas mentioned above.
More Answers:
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The Corollary of Polygon Angle-Sum Theorem: Discover the Relationship Between Interior Angles and Polygon Sides