Find the number of side of regular polygon whose each
Interior angle is a measure of 162°
Please answer this question
Sum of all the interior angles of any convex polygon of n sides is:
( 2 n - 4 ) ∙ 90°
Alsoo sum of n angles is n ∙ 162°
( 2 n - 4 ) ∙ 90° = n ∙ 162°
180° ∙ n - 360° = n ∙ 162°
Subtract n ∙ 162° to both sides
180° ∙ n - 162° ∙ n° - 360° = 0
18° ∙ n - 360° = 0
Add 360° to both sides
18° ∙ n = 360°
n = 360° / 18°
n = 20
To find the number of sides of a regular polygon where each interior angle measures 162°, we can use the formula for the interior angle of a regular polygon:
Interior Angle = (n - 2) * 180 / n
where n represents the number of sides of the polygon.
Given the interior angle measure as 162°, we can plug it into the formula and solve for n:
162 = (n - 2) * 180 / n
To simplify the equation, we can get rid of the fraction by multiplying both sides of the equation by n:
162n = (n - 2) * 180
Distribute the 180 on the right side:
162n = 180n - 360
Subtract 162n from both sides:
0 = 180n - 162n - 360
Combine like terms:
0 = 18n - 360
Add 360 to both sides:
360 = 18n
Divide both sides by 18:
20 = n
Therefore, a regular polygon with interior angles measuring 162° has 20 sides.