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Angles around Points & Lines

Exam code: 4024

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

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

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°

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

Solve to find $y$

$y = 180 - 123 y = 57$

$x = 25, y = 57$

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