Question

Given the regular polygon, what is the measure of each numbered angle? :)

Answer 1

it would be the third choice
72+72= 144 and then 144+72=180 degrees

Answer 2

Answer:

Option C is the correct choice.

Step-by-step explanation:

We have been given an image of a regular polygon. We are asked to find the measure of each numbered angle.

First of all we will find the measure of each interior angle of our given polygon using formula:

$\text{Each interior angle}=\frac{180(n-2)}{n}$, where n represents the sides of the regular polygon.

Since our polygon is a regular polygon with 10 sides, so each of its interior angle will be equal to:

$\text{Each interior angle}=\frac{180(10-2)}{10}$

$\text{Each interior angle}=18(8)$

$\text{Each interior angle}=144$

Since each of the interior angle of our given decagon is divided into two parts, so the measure of angle 2 and unnumbered angle will be half the 144 degrees.

$m\angle 2=\frac{144^{\circ}}{2}$

$m\angle 2=72^{\circ}$

Therefore, the measure of angle 2 is 72 degrees.

By angle sum property all the angles of a triangle add up-to 180 degree, so we can find measure of angle 1 as:

$m\angle 1+m\angle 2+\text{Measure of unnumbered angle}=180^{\circ}$

$m\angle 1+72^{\circ}+72^{\circ}=180^{\circ}$

$m\angle 1+144^{\circ}=180^{\circ}$

$m\angle 1+144^{\circ}-144^{\circ}=180^{\circ}-144^{\circ}$

$m\angle 1=36^{\circ}$

Therefore, the measure of angle 1 is 36 degrees.

Upon looking at our given choices we can see that option C is the correct choice.