Since we have here a regular heptagon, we have that the sum of the inner angles of this regular polygon is given by the formula:
(n - 2) * 180
We have that n = 7, then the sum of the inner angles is (7 - 2) * 180 = 5 * 180 = 900.
Since in this regular polygon, the angles and the sides are the same, then we have that the measure of each angle is:
900/7 = 128.571 degrees.
Then, we need to take each of the given equations and equate them to the latter value. Therefore, we have:
First Case:
5x + 5 = 128.571 ---> x = 24.7142
We have this value, because:
[tex]5x+5=128.571\Rightarrow5x=(128.571-5)\Rightarrow x=\frac{(123.571)}{5}\Rightarrow x=24.7142[/tex]
Second Case:
7x + 1 = 128.571 ---> x = 18.2244
We have this value, because:
[tex]7x+1=128.571\Rightarrow7x=128.571-1\Rightarrow x=\frac{127.571}{7}\Rightarrow x=18.2244[/tex]
Third Case:
x = 36.1631.
And this value is the result of:
[tex]\frac{7}{2}x+2=128.571\Rightarrow\frac{7}{2}x=128.57-2=126.571\Rightarrow x=\frac{2}{7}\cdot126.571=36.1631[/tex]
Therefore, we have that:
x = 24.7142 in
x = 18.2244 in
x = 36.1631 in < C (option 2)
