The size of each interior angle of a regular polygon is 168°. Find tge number of sides of the polygon
Let n be the number of sides of the regular polygon. Each interior angle of an n-sided polygon is given by the formula:
Interior angle = (n-2) × 180° / n
We are given that the size of each interior angle is 168°, so we can set up an equation:
168 = (n-2) × 180 / n
Multiplying both sides by n, we get:
168n = 180(n-2)
Expanding the right side, we get:
168n = 180n - 360
Subtracting 168n from both sides, we get:
12n = 360
Dividing both sides by 12, we get:
n = 30
Therefore, the regular polygon has 30 sides.
Calculate the size of one exterior angle of an 18 sided regular polygon
The sum of the exterior angles of a polygon is always 360°. For a regular polygon with n sides, each exterior angle has a size of:
Exterior angle = 360° / n
For an 18-sided regular polygon:
Exterior angle = 360° / 18 = 20°
Therefore, each exterior angle of an 18-sided regular polygon has a size of 20°.
To find the number of sides of a regular polygon given the measure of each interior angle, we can use the formula:
Number of sides = 360° / Measure of each interior angle
In this case, the given measure of each interior angle is 168°.
Using the formula, we can substitute the value into the formula:
Number of sides = 360° / 168°
Now, we can simplify the equation:
Number of sides = 2.143 ==> Since the number of sides must be a whole number, we round it up to the nearest whole number.
Therefore, the number of sides of the regular polygon is 3 (rounded up from 2.143).