What is the interior angle of a regular pentagon?
Understand the Problem
The question is asking for the measurement of the interior angle of a regular pentagon. To solve this, we can use the formula for calculating the interior angle of a regular polygon, which is (n-2) * 180° / n, where n is the number of sides.
Answer
$108^\circ$
Answer for screen readers
The interior angle of a regular pentagon is $108^\circ$.
Steps to Solve
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Identify the number of sides A regular pentagon has 5 sides. Thus, we have $n = 5$.
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Substitute into the formula We will use the formula for the interior angle of a regular polygon: $$ \text{Interior angle} = \frac{(n - 2) \cdot 180^\circ}{n} $$
By substituting $n = 5$ into the formula, we get: $$ \text{Interior angle} = \frac{(5 - 2) \cdot 180^\circ}{5} $$
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Calculate the numerator Calculate $(5 - 2) \cdot 180^\circ$: $$ (5 - 2) \cdot 180^\circ = 3 \cdot 180^\circ = 540^\circ $$
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Divide by the number of sides Now divide the result by the number of sides: $$ \text{Interior angle} = \frac{540^\circ}{5} $$
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Final calculation Perform the division: $$ \text{Interior angle} = 108^\circ $$
The interior angle of a regular pentagon is $108^\circ$.
More Information
The interior angle of each vertex of a regular pentagon is the same and equals $108^\circ$. This can help in various geometric calculations involving pentagons.
Tips
- Forgetting to subtract 2 from the number of sides ($n$) when applying the formula.
- Using the wrong formula; ensure you use the one specifically for regular polygons.
