Write an indirect proof in paragraph form.

Given: $\Delta XYZ;m\angle X=100$

Prove: $\angle Y$is not a right angle.

An indirect proof is a proof wherein you begin by assuming temporarily that the desired conclusion is not true which then by reasoning logically reaches to a certain contradiction or some other known fact.

1. Assume temporarily that the conclusion is not true.

2. Reason logically until you reach a contradiction.

3. Point out that the assumption was wrong and the conclusion must then be true.

Consider the following: $\Delta XYZ;m\angle X=100$

In order to write an indirect proof to prove that $\angle Y$is not a right angle assuming temporarily that the conclusion above is untrue and then work from there to finally conclude that the assumption is not true.

Proof: Assume temporarily that $\angle Y$is a right angle. Add the two angles $\angle X$and $\angle Y$and get:

$\begin{array}{c}\angle X+\angle Y=100°+90°\\ =190°\end{array}$

Since, it is known that the sum of angles is $180°$, so, initial assumption that $\angle Y$is a right angle is untrue.

Therefore, $\angle Y$is not a right angle.