Question

The measure of an interior angle of a regular polygon is 140°140°. find the number of sides of the polygon.

Answer 1

Answer: 9 sides

Step-by-step explanation: In this problem, we are given that the measure of each interior angle of a regular polygon is 140° and we are asked to find the number of sides of the polygon.

The measure of each interior angle of a regular polygon can be represented by the formula shown.

$\frac{180 (n-2)}{n}$

Since the measure of each interior angle of the given regular polygon is 140°, we can set our formula equal to 140.

$\frac{180 (n - 2)}{n} = 140$

The 'n' in the formula represents the number of sides of the polygon and the original question is asking for the number of sides of the polygon.

If we solve this equation for 'n', we will have our answer.

To solve this equation for 'n', we first need to get rid of the fraction on the left side of the equation so we multiply both sides of the equation by 'n'.

On the left side, the n's cancel out and we are left with 180 (n - 2) and on the right side we have 140n.

180 (n - 2) = 140n

Next, we distribute the 180 through the parentheses on the left side and we have 180n - 360 = 140n.

Next, we put our 'n' terms together on the right side of the equation by subtracting 180n from both sides and we have -360 = -40n.

Finally, we divide both sides of the equation by -40 and we find that 9 = n.

Therefore, if the measure of each interior angle of a regular polygon is 140°, then we known that the polygon has 9 sides.

Answer 2

$\alpha = \cfrac{180(n-2)}{n} \ \ \ \ \ [ \alpha =interior \ angle, \ \ n=number \ of \ sides] \\ \\ \\ 140 = \cfrac{180(n-2)}{n} \\ \\ 140n = 180(n-2) \\ \\ 140n=180n-360 \\ \\ 40n=360 \\ \\ n= \frac{360}{40}=9 \ \ sides$