Question

2 determine the measure of an interior angle of the given regular polygon. a regular nonagon b regular 15 - gon c regular decagon d regular 47 - gon

Explanation:

Step1: Recall the formula

The formula for the measure of an interior angle $\theta$ of a regular polygon with $n$ sides is $\theta=\frac{(n - 2)\times180^{\circ}}{n}$.

Step2: Solve for non - agon ($n = 9$)

Substitute $n = 9$ into the formula: $\theta=\frac{(9 - 2)\times180^{\circ}}{9}=\frac{7\times180^{\circ}}{9}=140^{\circ}$.

Step3: Solve for 15 - gon ($n = 15$)

Substitute $n = 15$ into the formula: $\theta=\frac{(15 - 2)\times180^{\circ}}{15}=\frac{13\times180^{\circ}}{15}=156^{\circ}$.

Step4: Solve for decagon ($n = 10$)

Substitute $n = 10$ into the formula: $\theta=\frac{(10 - 2)\times180^{\circ}}{10}=\frac{8\times180^{\circ}}{10}=144^{\circ}$.

Step5: Solve for 47 - gon ($n = 47$)

Substitute $n = 47$ into the formula: $\theta=\frac{(47 - 2)\times180^{\circ}}{47}=\frac{45\times180^{\circ}}{47}\approx172.34^{\circ}$.

Answer:

a. $140^{\circ}$
b. $156^{\circ}$
c. $144^{\circ}$
d. $\approx172.34^{\circ}$