Question - Solving for Number of Sides in a Regular Polygon
Solution:
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.
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