Question

write an indirect proof for the following conditional about the figure. if ∠efg and ∠hfj are vertical angles, then x≠3y. to prove the given conditional by contradiction, assume that ∠efg and ∠hfj are vertical angles and that x = 3y. because ∠efg and ∠hfj are vertical angles, they are congruent. this means their measures are equal, yielding the equation (type an equation using x and y as the variables. do not include the degree symbol in your answer. do not simplify.)

Explanation:

Step1: Recall vertical - angle property

Since vertical angles are congruent, the measure of ∠EFG is equal to the measure of ∠HFJ.

Step2: Set up the equation

The measure of ∠EFG is \(x + y\) and the measure of ∠HFJ is \(2x - y\). So the equation is \(x + y=2x - y\).

Answer:

\(x + y=2x - y\)