To determine the number of sides of a regular polygon based on its interior angle, we can use a simple mathematical formula. First, let's recall that the formula for each interior angle of a regular polygon with [tex]\( n \)[/tex] sides is given by:
[tex]\[ \text{Interior Angle} = \frac{(n - 2) \cdot 180^\circ}{n} \][/tex]
We can rearrange this formula to solve for [tex]\( n \)[/tex] when the interior angle is known. In this problem, the interior angle is given as 135°.
1. Set up the equation with the given interior angle:
[tex]\[ 135 = \frac{(n - 2) \cdot 180}{n} \][/tex]
2. Multiply both sides by [tex]\( n \)[/tex] to get rid of the fraction:
[tex]\[ 135n = (n - 2) \cdot 180 \][/tex]
3. Distribute the 180 on the right side:
[tex]\[ 135n = 180n - 360 \][/tex]
4. Move all terms involving [tex]\( n \)[/tex] to one side by subtracting [tex]\( 180n \)[/tex] from both sides:
[tex]\[ 135n - 180n = -360 \][/tex]
[tex]\[ -45n = -360 \][/tex]
5. Solve for [tex]\( n \)[/tex] by dividing both sides by -45:
[tex]\[ n = \frac{360}{45} \][/tex]
[tex]\[ n = 8 \][/tex]
So, the number of sides of the regular polygon is 8.
Therefore, the correct answer is:
B. 8 sides
