EDEXCEL GCSE FOUNDATION MATHS - What are Angles in Polygons

Edexcel GCSE Foundation Maths: What are Angles in Polygons?

Introduction:

Polygons are closed shapes made up of straight line segments. Angles play a crucial role in understanding and working with polygons. In this tutorial, we'll explore what angles are in polygons and how to calculate them.

Key Concepts:

• Angle: An angle is formed by two lines that meet at a point called the vertex. We measure angles in degrees (°).
• Polygon: A closed shape formed by straight line segments.
• Interior Angle: An angle inside a polygon formed by two adjacent sides.
• Exterior Angle: An angle formed by one side of a polygon and the extension of the adjacent side.

Types of Polygons:

• Triangle: A polygon with three sides and three angles.
• Quadrilateral: A polygon with four sides and four angles.
• Pentagon: A polygon with five sides and five angles.
• Hexagon: A polygon with six sides and six angles.
• Heptagon: A polygon with seven sides and seven angles.
• Octagon: A polygon with eight sides and eight angles.

Angle Properties of Polygons:

• Sum of Interior Angles: The sum of the interior angles of a polygon can be calculated using the formula: (n - 2) × 180° where 'n' is the number of sides of the polygon.

• Sum of Exterior Angles: The sum of the exterior angles of any polygon is always 360°.

Examples:

• Triangle:
• Sum of interior angles: (3 - 2) × 180° = 180°
• Quadrilateral:
• Sum of interior angles: (4 - 2) × 180° = 360°
• Pentagon:
• Sum of interior angles: (5 - 2) × 180° = 540°

Example Problems:

1. Find the missing angle in a triangle:

2. If two angles of a triangle are 50° and 70°, the third angle can be found by: 180° - 50° - 70° = 60°

3. Find the sum of interior angles of a hexagon:

4. Using the formula: (6 - 2) × 180° = 720°

Tips for Solving Polygon Angle Problems:

• Remember the formulas: The formula for the sum of interior angles is crucial.
• Draw diagrams: Visual representation can help understand the problem better.
• Identify the given information: Note down the known angles and sides.
• Apply the angle properties: Use the properties of interior and exterior angles to solve the problem.

Practice Questions:

1. Calculate the sum of the interior angles of a heptagon.
2. Find the missing angle in a quadrilateral if three of its angles are 90°, 110°, and 70°.
3. What is the value of each exterior angle of a regular hexagon?

Conclusion:

Understanding angles in polygons is essential for working with various geometric problems. By applying the formulas and properties discussed in this tutorial, you can confidently solve problems involving angles in polygons. Remember to practice regularly and refer to resources for further clarification.