Prove the given conditional statement is true by contradiction

Question

If m∠F = 100° and ∠F and ∠G are supplementary, then m∠G = 80°, how would you prove this using contradiction?

Answer 1

Start by stating to opposite of the conclusion. So:

Assume m∠G ≠ 80°

We are told ∠F and ∠G are supplementary (given)

That implies m∠F + m∠G = 180° (definition of supplementary)

Since m∠G ≠ 80°, because m∠F + m∠G = 180°, then m∠F ≠ 100°

But that contradicts the original given that m∠F = 100°

Therefore, by contradiction, our original assumption (m∠G ≠ 80°) is not true. If it is not true, then m∠G MUST equal 80° and, if so, the given conditional statement is true.