4.5.4

Opposite Angles in Cyclic Quadrilaterals

Test yourself

Circle Theorems

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Opposite angles in a cyclic quadrilateral

  • Opposite angles in a cyclic quadrilateral add up to 180°.
    • Here x + y = 180°
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Proof

  • Label the opposite angles, then draw two radii from the other corners.
  • Use ‘angle at centre twice that at the circumference’ to get the angles at the centre as 2x, 2y.
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Proof continued

  • Since angles at a point add up to 360°:
    • 2x + 2y = 360° and so x + y = 180°.

Jump to other topics

1Number

1.1Using Numbers

1.2Fractions, Decimals & Percentages

1.3Powers & Roots

1.4Accuracy

2Algebra

2.1Introduction to Algebra

2.2Manipulating Algebra

2.3Proofs & Functions

2.4Straight Line Graphs

2.5Common Graphs

2.6Transformations & Tangents

2.7Properties of Graphs

2.8Solving Equations

2.9Inequalities

2.10Sequences

3Ratio

4Geometry

4.1Introduction to Geometry

4.2Triangles & Quadrilaterals

4.3Transformations

4.4Circle Basics

4.5Circle Theorems

4.6Measurements & Units

4.7Calculating Area

4.8Triangle Formulae

4.93D Shapes

4.10Vectors

5Probability

6Statistics

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