Rukasha Maths

GCSE maths Beta

Angles and bearings · Revision guide

Foundation · Geometry · 2 pages in the PDF

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Learning objectives

  • Use angle facts to calculate missing angles.
  • Measure and interpret three-digit bearings.

Key ideas

Use straight-line, full-turn and triangle angle totals.

straight line: 180∘,point: 360∘,triangle: 180∘\text{straight line: }180^\circ,\quad\text{point: }360^\circ,\quad\text{triangle: }180^\circ

For parallel lines, corresponding and alternate angles are equal; co-interior angles are supplementary.

The interior angle sum depends on the number of polygon sides.

S=(n−2)180∘S=(n-2)180^\circ

For a regular polygon, exterior angles are equal.

each exterior angle=360∘n\text{each exterior angle}=\frac{360^\circ}{n}

Measure bearings clockwise from north at the starting point. Write three digits.

Worked examples

Example 1

Find the return bearing for a journey with the given outward bearing.

outward bearing=065∘\text{outward bearing}=065^\circ

The return direction differs by half a turn.

65∘+180∘=245∘65^\circ+180^\circ=245^\circ
245∘245^\circ

Example 2

Find each exterior angle of a regular octagon.

360∘8=45∘\frac{360^\circ}{8}=45^\circ
45∘45^\circ

Watch out

Bearings start at north at the starting point. For a return bearing, add or subtract half a turn as appropriate.