a) The exterior angle of a regular polygon is 20°. Find the number of sides of this regular polygon. b) Write down the mathematical name for a 5-sided polygon.

Understand the Problem

The question is asking for two parts: (a) to calculate the number of sides of a regular polygon given its exterior angle of 20°, and (b) to name the mathematical term for a polygon with five sides.

Answer

(a) $18$; (b) Pentagon

Steps to Solve

Understanding the relationship between exterior angles and sides

For a regular polygon, the total number of degrees in the exterior angles is always $360^\circ$. The exterior angle can be calculated using the formula:

$$ \text{Exterior Angle} = \frac{360^\circ}{n} $$

where $n$ is the number of sides.

Setting up the equation

Given that the exterior angle is $20^\circ$, we set up the equation:

$$ 20^\circ = \frac{360^\circ}{n} $$

Solving for the number of sides

To find $n$, we can rearrange the equation:

$$ n = \frac{360^\circ}{20^\circ} $$

Now, we can calculate the value of $n$.

Calculating the result

Perform the division:

$$ n = \frac{360}{20} = 18 $$

Thus, the polygon has 18 sides.

Naming the polygon with five sides

The mathematical term for a polygon with five sides is a "pentagon".

(a) The number of sides of the polygon is $18$.

(b) The mathematical name for a five-sided polygon is "pentagon".

More Information

Polygons are named based on the number of their sides. A pentagon, for example, has five sides and five angles. Regular polygons have equal-length sides and equal angles.

Tips

Forgetting the relationship between exterior angles and sides can lead to incorrect calculations. Always remember that the sum of all exterior angles in any polygon is $360^\circ$.
Confusing exterior angles with interior angles. It's crucial to distinguish between them when solving for the number of sides.

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