EDEXCEL GCSE FOUNDATION MATHS - What are Angles in a Quadrilateral

EDEXCEL GCSE Foundation Maths - What are Angles in a Quadrilateral?

Introduction

A quadrilateral is a four-sided shape. The angles inside a quadrilateral always add up to 360°.

Key Terms:

• Quadrilateral: A four-sided shape.
• Angle: The space between two lines that meet at a point.
• Interior Angle: The angle inside a shape.

Understanding the Concept

Imagine you have a quadrilateral. If you add up all four of the interior angles, you will always get 360°. This is true for all quadrilaterals, regardless of their shape or size.

Example

Let’s look at a rectangle:

• Rectangle: A quadrilateral with four right angles.
• Right Angle: An angle that measures 90°.

In a rectangle, each angle is a right angle (90°). So, the total sum of the angles is:

90° + 90° + 90° + 90° = 360°

Formula

The sum of interior angles of a quadrilateral is represented by the formula:

Sum of interior angles = 360°

Applications

Knowing the sum of angles in a quadrilateral is important for:

• Solving problems involving unknown angles: You can use the formula to find missing angles in a quadrilateral.
• Understanding the properties of different quadrilaterals: Knowing the sum of angles helps you understand the relationships between different types of quadrilaterals, like squares, rectangles, parallelograms, and trapezoids.

Practice

1. Find the missing angle in the quadrilateral below:

• Solution:
  • Add the three known angles: 100° + 70° + 110° = 280°
  • Subtract the sum from 360° to find the missing angle: 360° - 280° = 80°
  • The missing angle is 80°.

1. A square has four equal sides and four right angles. What is the sum of its interior angles?

• Solution:
  • Since each angle in a square is a right angle (90°), the sum of the interior angles is: 90° + 90° + 90° + 90° = 360°.

Summary

Understanding the concept of angles in a quadrilateral is crucial for solving geometry problems and understanding the properties of various quadrilaterals. Remember that the sum of interior angles in any quadrilateral will always equal 360°.