Angles on a straight line
Angles that sit next to each other on a straight line add up to 180°.
Total = 180°
Example: If one angle is 125°, the missing angle is 180° − 125° = 55°.
[ SYSTEM ONLINE ] YEAR 8 // REVISION
Angles &
Angles &
Geometry
Year 8 revision in one place: the key rules, worked examples, a formula sheet, a podcast to listen to and a self-marking quiz.
∑ 180°
360° ↻
SYS.VISUAL // TRIANGLE_01
01 / The foundations
Angle essentials
Start here: these rules appear throughout geometry.
Angles around a point
All the angles around one point make a complete turn.
Total = 360°
Example: If three angles are 100°, 120° and x°, then x = 360° − 220° = 140°.
Vertically opposite angles
When two straight lines cross, the angles directly opposite each other are equal.
Opposite angles are equal
Example: If one angle is 120°, the angle directly opposite is also 120°. The two neighbouring angles are 60° each.
How to choose the rule
Look at the whole diagram before calculating.
- A straight line? Think 180°.
- A complete turn around a point? Think 360°.
- Two lines crossing? Opposite angles are equal.
02 / Parallel lines
Angles in parallel lines
A transversal is a line that crosses two or more other lines.
Corresponding angles
Corresponding angles occupy the same relative position where the transversal crosses each parallel line.
Corresponding angles are equal
Look for matching positions
Alternate angles
Alternate angles lie between the parallel lines and on opposite sides of the transversal.
Alternate angles are equal
Opposite sides of the transversal
Co-interior angles
Co-interior angles lie between the parallel lines and on the same side of the transversal.
Co-interior total = 180°
Same side of the transversal
Important exam reminder
These parallel-line rules depend on the two lines being parallel. Look for matching arrow markings in the diagram.
Use the full names: corresponding, alternate and co-interior angles.
03 / Three-sided shapes
Triangles
The interior angles of every triangle add up to 180°.
Triangle angle sum
A + B + C = 180°
Example: Two angles are 35° and 85°. The third is 180° − 35° − 85° = 60°.
Isosceles triangle
An isosceles triangle has two equal sides. The angles opposite those sides are also equal.
2 equal sides2 equal base anglesEquilateral triangle
An equilateral triangle has three equal sides and three equal interior angles.
Each angle = 60°
180° ÷ 3 = 60°.
Triangle problem strategy
- Write down the angles you know.
- Subtract their total from 180°.
- Use equal-side or equal-angle information if it is isosceles or equilateral.
- Check that all three angles total 180°.
04 / Many-sided shapes
Interior & exterior angles
A polygon is a closed 2D shape made from straight sides.
Interior and exterior angles
Interior angle: an angle inside the polygon.
Exterior angle: the angle formed outside when one side is extended.
Interior + adjacent exterior = 180°
Exterior angles of a polygon
If you walk around a convex polygon, the turns add up to one complete turn.
Exterior angles total = 360°
Regular polygons
A regular polygon has all sides equal and all interior angles equal.
Each exterior angle = 360° ÷ n
Number of sides n = 360° ÷ exterior angle
Example: A regular octagon has 8 sides. Each exterior angle is 360° ÷ 8 = 45°.
Sum of interior angles
Drawing diagonals from one vertex of a convex polygon divides it into n − 2 triangles.
Interior sum = 180° × (n − 2)
Example: A pentagon has 5 sides, so its interior angle sum is 180° × (5 − 2) = 540°.
05 / One-glance revision
The geometry cheat sheet
The rules worth knowing confidently.
180°Straight line
360°Around a point
EqualVertically opposite
EqualCorresponding
EqualAlternate
180°Co-interior total
180°Triangle angle sum
60° eachEquilateral triangle
360°Polygon exterior sum
06 / AUDIO REVISION
🎧 THE GEOMETRY FREQUENCY
Your revision, remixed. Put your headphones on and let the angle rules sink in.
NOW PLAYING · GEOMETRY REVISION
Angles, lines & polygons
MP3
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07 / Check your understanding
Quick knowledge check
Have a go without looking at the notes first.