Angle Relationships

Angles that sit together follow fixed rules:

• Complementary angles add to $90°$. The complement of $35°$ is $90 - 35 = 55°$.
• Supplementary angles add to $180°$. The supplement of $110°$ is $180 - 110 = 70°$.
• Angles on a straight line add to $180°$; angles around a point add to $360°$.
• Vertically opposite angles (the pair opposite each other where two lines cross) are equal.

When two parallel lines are cut by a straight line, corresponding angles are equal and alternate angles are equal — worth recognising, though the four rules above cover most problems.

Exam checkpoint

Angle facts are relationships, not separate facts to memorise. Angles on a straight line total $180^\circ$; angles around a point total $360^\circ$; vertically opposite angles are equal. Mark the diagram with each fact you use so the reason for a calculation is visible.

Short worked example. If one angle on a straight line is $68^\circ$, its neighbour is $180-68=112^\circ$. The two angles form a straight line.