Answer:
Explained below.
Step-by-step explanation:
The formula for the interior angle of any regular polygon is given as;
Interior Angle = 180(n - 2)/n
Where n is number of sides
We are told the interior angle is 40°
Thus;
180(n - 2)/n = 40
Cross multiply to get;
180n - 360 = 40n
180n - 40n = 360
140n = 360
n = 360/140
n = 2.57
Number of sides of a regular polygon cannot be in decimal nor can it have less than 3 sides.
Thus, a shape with interior angle of 40 cannot be a polygon.
There is no regular polygon that has just 2 sides, therefore, a regular polygon cannot have an interior angle that is 40°.
The sum of all the interior angles of a regular polygon is given as, (n - 2)180.
Thus, assuming an interior angle is 40°, thus, let's find out if there is any regular polygon that has an interior angle that measures 40° using the formula, (n - 2)180.
Thus:
(n - 2)180 = 40
180n - 360 = 40
180n = 40 + 360
180n = 400
n = 400/180
n = 2.22
Thus, there is no regular polygon that has just 2 sides, therefore, a regular polygon cannot have an interior angle that is 40°.
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