To solve for the number of sides of a regular polygon given that each interior angle is 168°, we can use the relationship that defines the interior angle of a regular polygon. The formula for the interior angle [tex]\( \theta \)[/tex] of a regular polygon with [tex]\( n \)[/tex] sides is given by:
[tex]\[ \theta = \frac{(n-2) \times 180^\circ}{n} \][/tex]
We are given that [tex]\( \theta = 168^\circ \)[/tex], so we can set up the equation:
[tex]\[ 168 = \frac{(n-2) \times 180}{n} \][/tex]
First, let's simplify and solve for [tex]\( n \)[/tex].
1. Multiply both sides by [tex]\( n \)[/tex] to eliminate the fraction:
[tex]\[ 168n = (n-2) \times 180 \][/tex]
2. Distribute the 180:
[tex]\[ 168n = 180n - 360 \][/tex]
3. Move all terms involving [tex]\( n \)[/tex] to one side and constants to the other side:
[tex]\[ 180n - 168n = 360 \][/tex]
[tex]\[ 12n = 360 \][/tex]
4. Solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{360}{12} \][/tex]
[tex]\[ n = 30 \][/tex]
Therefore, the number of sides of the polygon is [tex]\( 30 \)[/tex].
So the correct answer is:
A. 30
