Solving for Number of Sides in a Regular Polygon
To solve this problem, you can use the formula that relates the number of sides of a regular polygon (n) to the measure of its interior angles (A):
\[ A = \frac{(n - 2) \times 180°}{n} \]
Given that \( A = 140° \), you will need to set up the equation to solve for n:
\[ 140° = \frac{(n - 2) \times 180°}{n} \]
Multiply both sides by n to clear the fraction:
\[ 140n = (n - 2) \times 180 \]
Distribute the 180° across the (n - 2):
\[ 140n = 180n - 360 \]
Then, subtract 180n from both sides to solve for n:
\[ -40n = -360 \]
Divide both sides by -40:
\[ n = \frac{-360}{-40} \]
\[ n = 9 \]
Therefore, the regular polygon has 9 sides.
