As we have already seen in Naming Angles, there are two special angle types called supplementary and complementary. Apart from just being able to recognise them when we see them, we also need to know how to solve angle problems that use these special angle relationships.
Supplementary angles are two angles that sum to $180$180°. In the diagram, $\angle COD$∠COD and $\angle DOE$∠DOE are supplementary angles. You might see supplementary angles as two angles that add up to a straight line.
Adjacent angles on a straight line are supplementary (sum to 180°)
Complementary angles are two angles that sum to $90$90°. In the diagram, $\angle DOC$∠DOC and $\angle COB$∠COB are complementary. You might see complementary angles as two angles that add up to a right angle.
Adjacent angles forming a right angle are complementary (sum to 90°)
Let's have a look at these worked examples.
Calculate $x$x giving reasons for your answer.
Calculate $x$x giving reasons.
In the diagram, $AB$AB is a straight line.
Solve for $x$x. Give reasons.