Questions: An interior angle of a regular convex polygon is 140°. How many sides does the polygon have? A. 8 B. 9 C. 10 D. 11

Solution Steps

To find the number of sides of a regular convex polygon given an interior angle, we can use the formula for the interior angle of a regular polygon: \((n-2) \times 180^\circ / n = \text{interior angle}\), where \(n\) is the number of sides. Rearrange this formula to solve for \(n\).

The formula for the interior angle \( A \) of a regular polygon with \( n \) sides is given by:

\[ A = \frac{(n-2) \times 180^\circ}{n} \]

Given that the interior angle \( A = 140^\circ \), we can set up the equation:

\[ 140 = \frac{(n-2) \times 180}{n} \]

To eliminate the fraction, multiply both sides by \( n \):

\[ 140n = (n-2) \times 180 \]

Expanding the right side gives:

\[ 140n = 180n - 360 \]

Rearranging the equation to isolate \( n \):

\[ 180n - 140n = 360 \]

This simplifies to:

\[ 40n = 360 \]

Dividing both sides by 40 yields:

\[ n = \frac{360}{40} = 9 \]

Final Answer