The degree measure of one angle of 36 sided regular polygon is 170.
Polygon
Regular polygon means:
- Straight sides
- Have equal length in all sides
- Have equal degree in all angles
If there is a 36-sided regular polygon, that means there is 36 sides and 36 angles that have same length and degree.
To calculate the degree measure of one angle is:
- Imagine, polygon is a set of isosceles triangles, where the peak of triangles are put together in the middle. (You can see pentagon in the picture). The number of triangles are same as the number of pentagon's sides. In this question, there are 36 triangles.
- The sum of angles of triangle is 180. The sum of angles of all triangle means
Number of side x 180
36 x 180 = 6480.
- Remember, the peak of the triangle is put together in the middle. So the sum of angles of all triangle not same with sum of angles of pentagon. We must subtract it with 360.
(Number of side x 180) - 360
6480 - 360 = 6120
- There is 36 sides in the pentagon, so the degree of one angle is
(Number of side x 180) - 360
Number of side
6120/36 = 170
We can also simplify the formula
(Number of side x 180) - 360 = 180 - 360 ____
Number of side Number of side
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