Three regular polygons fit exactly together around a point on a plane. One is a square and another is a hexagon. How many sides does the third polygon have?
Answers
Step-by-step explanation:
sum of interior angle of polygon = (n-2) *180 ... (1)
there is square and hexagon which has interior angle 90 and 120 which sum 210 around one point so space remaining for other polygon interior angle is 150.
sum of interior angle of polygon = n* measure of one interior angle .... (2)
in polygon
number of angle=number of sides......(3)
from (1) (2) (3)
150*n = (n-2) *180
n=12
The hexagon provides 120 degrees, the square 90 degrees. It takes 360 degrees to go all around a circle, so the missing polygon has angles of 150 degrees (360 - (120 + 90)).
To find the measures of the angles of a regular n-sided polygon, we use the formula:
180(n - 2) / n
In this case, we know the angle measure, we’re just looking for n. So we have the equation:
150 = 180(n - 2) / n
n = 180(n - 2) / 150
n = 1.2(n - 2)
n = 1.2n - 2.4
-0.2n = -2.4
n = 12
The third polygon has 12 sides.