Angles around Points & Lines (Cambridge International IGCSE Mathematics)

Basic Angle Properties

What are the basic angle properties?

• Angles around a point add up to 360°

• Angles that form a straight line add up to 180°

• Vertically opposite angles are equal

  • Vertically opposite angles occur when two lines intersect, as in the diagram below

Vertically opposite angles

Exam Hint Use the angle properties to find any missing angles that you can, and mark them on the diagram

• Even if they are not the angle you are trying to find, they may help provide a clue!

Worked Example The diagram below shows three straight lines intersecting at a point.

Find the values of $x$ and $y$.

Answer:

Vertically opposite angles between two intersecting lines are equal

$x=25$

Angles that meet on a straight line add up to 180°

$\begin{gathered} x + y + 98 & = 180 \\ 25 + y + 98 & = 180 \\ 123 + y & = 180 \end{gathered}$

Solve to find $y$

$y=180-123\,y=57$

$x=25,y=57$