Interior Angles Of A Polygon- GCSE Maths - Steps & Examples - Free Printable

The image provides a structured approach to solving problems involving the interior angles of polygons. Let's break down the steps and explain how to apply them:

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Steps to Solve Problems Involving Interior Angles of Polygons

1. Identify the number of sides in any polygon(s) given in the question
- Determine how many sides the polygon has. This is crucial because the number of sides directly affects the sum of the interior angles.
- Note whether the polygon is regular (all sides and angles are equal) or irregular (sides and angles may vary).

2. Find the sum of interior angles for any polygon(s) given
- Use the formula for the sum of the interior angles of a polygon:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon.
- For example:
- A triangle (\( n = 3 \)): \((3 - 2) \times 180^\circ = 180^\circ\)
- A quadrilateral (\( n = 4 \)): \((4 - 2) \times 180^\circ = 360^\circ\)
- A pentagon (\( n = 5 \)): \((5 - 2) \times 180^\circ = 540^\circ\)

3. Identify what the question is asking
- Understand what the problem requires you to find. Common questions include:
- The sum of the interior angles.
- The measure of one interior angle in a regular polygon.
- Finding a missing angle in an irregular polygon.
- Determining the number of sides of a polygon based on the sum of its interior angles.

4. Solve the problem using the information you have already gathered
- Apply the relevant formulas and logical reasoning to solve the problem.
- For a regular polygon, the measure of one interior angle can be found using:
\[
\text{Measure of one interior angle} = \frac{\text{Sum of interior angles}}{n}
\]
- For an irregular polygon, use the given angles and the sum of interior angles to find missing angles.

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Example Problem and Solution

#### Problem:
A regular hexagon has six equal sides. What is the measure of one interior angle?

#### Solution:
1. Identify the number of sides:
- The polygon is a hexagon, so \( n = 6 \).

2. Find the sum of interior angles:
- Use the formula:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ = (6 - 2) \times 180^\circ = 4 \times 180^\circ = 720^\circ
\]

3. Identify what the question is asking:
- The question asks for the measure of one interior angle in a regular hexagon.

4. Solve the problem:
- Since the hexagon is regular, all interior angles are equal. Divide the sum of the interior angles by the number of sides:
\[
\text{Measure of one interior angle} = \frac{\text{Sum of interior angles}}{n} = \frac{720^\circ}{6} = 120^\circ
\]

#### Final Answer:
\[
\boxed{120^\circ}
\]

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Key Takeaways

- Always start by identifying the number of sides and whether the polygon is regular or irregular.
- Use the formula \((n - 2) \times 180^\circ\) to find the sum of the interior angles.
- For regular polygons, divide the sum of the interior angles by the number of sides to find the measure of one angle.
- For irregular polygons, use the given angles and the sum of interior angles to solve for missing angles.

This structured approach ensures clarity and accuracy in solving problems involving interior angles of polygons.