Question

question 48 of 50
read the following conditional statement: if $\angle a$ and $\angle b$ are supplements, then $\angle a$ and $\angle b$ cannot both be obtuse. which of the following choices is the first step of an indirect proof for the statement?
\bigcirc\quad assume $\angle a$ and $\angle b$ are acute
\bigcirc\quad assume $\angle a$ and $\angle b$ are not supplements
\bigcirc\quad assume $\angle a$ and $\angle b$ are both obtuse

Explanation:

In an indirect proof (proof by contradiction), we assume the negation of the conclusion. The conclusion of the conditional statement "If ∠A and ∠B are supplements, then ∠A and ∠B cannot both be obtuse" is "∠A and ∠B cannot both be obtuse". The negation of this is "∠A and ∠B are both obtuse", so we assume this for the indirect proof.

Answer:

Assume ∠A and ∠B are both obtuse (the third option)