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

Mathematics

2 answers:

Inessa [12.5K]2 months ago

5 0

Response:

The right choice is option C.

Explanation in detail:

We were presented with an illustration of a regular polygon and tasked with determining the measure of each numbered angle.

Initially, we need to calculate the measure of every interior angle of the given polygon using the formula:

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

Given that our polygon is regular and has 10 sides, the measurement for each interior angle will equal:

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

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

$\text{Each interior angle}=144$

Since the interior angle of our decagon splits into two sections, the measures for angle 2 and the unnamed angle will be half of 144 degrees.

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

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

Thus, angle 2 measures 72 degrees.

According to the angle sum property, all triangle angles total 180 degrees, enabling us to determine the measurement 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, angle 1 is 36 degrees.

Reviewing the available choices confirms that option C is indeed correct.

PIT_PIT [12.4K]2 months ago

4 0

It should be the third option
72+72= 144 and subsequently 144+72=180 degrees

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