You discovered that if a pair of angles is a linear pair, then the angles are supplementary. Does that mean that all supplementary angles form a linear pair of angles? Is the converse true? If not, sketch a counterexample.

Question

You discovered that if  a pair of  angles is a linear pair, then the angles are supplementary. Does that mean that all supplementary angles form a linear pair of  angles? Is the converse true? If  not, sketch a counterexample.

anonymous · Answer

No, not all supplementary angles are a linear pair.

A counterexample is: three angles can add up to 180 degrees but that wouldn't be a linear pair.

A linear pair is when TWO angles add up to 180.

Supplementary angles can also be linear pair but supplementary angles also apply when more than two angles add up to 180.

All linear pairs are supplementary angles, but not all supplementary angles are linear pairs.