Question

the measure of each interior angle of a regular polygon is 140°. find the number of sides.
number of sides =

Explanation:

Step1: Recall the formula for interior angle of a regular polygon

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( I=\frac{(n - 2)\times180^{\circ}}{n} \), where \( I \) is the measure of each interior angle. We know that \( I = 140^{\circ} \), so we set up the equation:

$$ 140=\frac{(n - 2)\times180}{n} $$

Step2: Solve the equation for \( n \)

First, multiply both sides of the equation by \( n \) to get rid of the denominator:

$$ 140n=(n - 2)\times180 $$

Expand the right - hand side:

$$ 140n = 180n-360 $$

Subtract \( 140n \) from both sides:

$$ 0 = 180n-140n - 360 $$

Simplify the right - hand side:

$$ 0 = 40n-360 $$

Add 360 to both sides:

$$ 40n=360 $$

Divide both sides by 40:

$$ n=\frac{360}{40}=9 $$

Answer:

9