Angle Rules
Grade 3The basic angle facts
A few simple rules cover most angle questions at GCSE. They are not complicated — you just need to know them by name so you can quote them in proofs.
Angles on a straight line add up to 180°. Angles around a point add up to 360°. Vertically opposite angles are equal — they are the pair of angles formed across the crossing point when two lines intersect.
Angles in triangles and quadrilaterals
The angles inside any triangle add up to 180°. The angles inside any quadrilateral add up to 360°. These follow directly from the straight-line rule once you draw a diagonal.
Special triangles worth knowing: an equilateral triangle has three 60° angles; an isosceles triangle has two equal base angles.
Worked example
Don't mix up the rules
Try this one
The diagram shows a straight line XY and two lines PA and QB that are parallel to each other. A transversal meets PA at point G and QB at point H. Angle PGH = \( (9k - 5)^\circ \) and angle GHB = \( (6k + 25)^\circ \).
Angle PGH and angle GHB are alternate angles.
Find the value of \( k \) and the size of angle GHB. [4]
The question tells you these are alternate angles between parallel lines.
Ask yourself: 'What is always true about alternate angles — do they add to 180° or are they equal to each other?' Use that fact to set up an equation, then solve for k and substitute back.
