① Angles on a line & at a point
Angles on a straight line add up to \(180^\circ\). Angles all the way round a point add up to \(360^\circ\). Use the angles you're given to find the missing one \(x\) — and be ready to say why.
② Angles in triangles
The three angles in any triangle add up to \(180^\circ\). Some triangles below are isosceles — tick marks show the two equal sides, and the two base angles they create are equal.
③ Angles in parallel lines
The arrows show which lines are parallel. A transversal crosses them, making pairs of angles that are either equal or add up to \(180^\circ\), depending on where they sit — sometimes with a third parallel line to read carefully.
Key rules — always give a reason
Angles on a straight line add up to \(180^\circ\).
Angles round a point add up to \(360^\circ\).
Vertically opposite angles (across a crossing of two lines) are equal.
Angles in a triangle add up to \(180^\circ\). Base angles in an isosceles triangle are equal.
Exterior angle of a triangle = the sum of the two opposite (remote) interior angles.
Parallel lines: corresponding angles are equal; alternate angles are equal; co-interior angles add up to \(180^\circ\).
A numerical answer on its own is not enough — always name the rule you used, e.g. "vertically opposite angles" or "co-interior angles".