A quadrilateral's four angles add up to 360°, not 180° — a quadrilateral is two triangles, so it is 180 × 2. The special quadrilaterals give you shortcuts on top of that: in a parallelogram and a rhombus, opposite angles are equal and neighbouring angles add to 180°. In the hardest questions a triangle and a quadrilateral share an angle, so the angle you find first is the one that unlocks the second shape.
Worked example
Problem In quadrilateral PQRS, angle P = 80°, angle Q = 95° and angle R = 110°. Find angle S.
The four angles of any quadrilateral add up to 360°.
Add the three you are given: 80 + 95 + 110 = 285.
So angle S is 360 − 285 = 75°.
Watch out Four sides means 360°. Subtracting from 180 is the commonest slip.