Answer:
n = 9
Step-by-step explanation:
As angles around a point sum to 360°, we can set up the following equation and solve for x:
[tex]8x^{\circ} + 7x^{\circ} + 3x^{\circ}=360^{\circ}\\\\\\8x+7x+3x=360\\\\\\18x=360\\\\\\x=\dfrac{360}{18}\\\\\\x=20[/tex]
Now, calculate the measure of the interior angle of regular polygon B by substituting x = 20 into the angle expression 7x°:
[tex]7x^{\circ}=7(20)^{\circ}=140^{\circ}[/tex]
To determine the number of sides (n) of regular polygon B, we can use the following formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Interior angle of a regular polygon}}\\\\\theta=\dfrac{180^{\circ}(n-2)}{n}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the interior angle.}\\\phantom{ww}\bullet\;\textsf{$n$ is the number of sides.}\end{array}}[/tex]
Substitute θ = 140° into the formula and solve for n:
[tex]140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\\\\\\140^{\circ}n=180^{\circ}(n-2)\\\\\\140n=180(n-2)\\\\\\140n=180n-360\\\\\\140n+360=180n-360+360\\\\\\140n+360=180n\\\\\\140n+360-140n=180n-140n\\\\\\360=40n\\\\\\\dfrac{40n}{40}=\dfrac{360}{40}\\\\\\n=9[/tex]
Therefore, the number of sides (n) of polygon B is:
[tex]\LARGE\boxed{\boxed{n=9}}[/tex]
