The measure of each exterior angle of a regular polygon of 5 sides is equal to

Question

Accepted Answer

The correct option is 2:

To solve this problem, we need to recall a fundamental property of polygons: the sum of the measures of the exterior angles of any convex polygon is always $360^{\circ}$. This holds true regardless of the number of sides the polygon has.

For a regular polygon, all its sides are equal in length, and all its interior angles are equal in measure. Consequently, all its exterior angles are also equal in measure.

Given a regular polygon with 'n' sides, the measure of each exterior angle can be found by dividing the total sum of exterior angles ($360^{\circ}$) by the number of sides 'n'.

Step 1: Identify the given information.
The polygon is a regular polygon.
The number of sides of the polygon, $n = 5$.

Step 2: Recall the formula for the measure of each exterior angle of a regular polygon.
The measure of each exterior angle $= \frac{	ext{Sum of exterior angles}}{	ext{Number of sides}}$
Since the sum of exterior angles of any polygon is $360^{\circ}$, the formula becomes:
Measure of each exterior angle $= \frac{360^{\circ}}{n}$

Step 3: Substitute the number of sides into the formula and calculate.
Measure of each exterior angle $= \frac{360^{\circ}}{5}$
Measure of each exterior angle $= 72^{\circ}$

Step 4: Compare the calculated value with the given options.
Our calculated value is $72^{\circ}$, which matches Option 2.

The incorrect option is 1: This option might arise if there was a misunderstanding of the formula or a calculation error. For example, if one mistakenly used $180^{\circ}$ instead of $360^{\circ}$ as the sum of exterior angles and divided by 5, or if there was a different incorrect division.

The incorrect option is 3: This option represents an exterior angle of a regular quadrilateral (square), where $\frac{360^{\circ}}{4} = 90^{\circ}$. It is incorrect for a 5-sided polygon.

The incorrect option is 4: This option might be a result of a calculation error or an incorrect formula. For instance, if one thought the sum was $180^{\circ}$ and divided by 4, or another miscalculation.