Question

∠v and ∠x are supplementary and ∠w and ∠v are supplementary. complete the proof that ∠x≅∠w.
statement\treason
1 ∠v and ∠x are supplementary\tgiven
2 ∠w and ∠v are supplementary\tgiven
3 m∠v + m∠x = 180°\tdefinition of supplementary angles
4 m∠w + m∠v = 180°\tdefinition of supplementary angles
5 m∠v + m∠x = m∠w + m∠v\ttransitive property of equality
6 m∠x = m∠w\t
7 ∠x≅∠w\tdefinition of congruence

Explanation:

Step1: Recall the given equations

We have $m\angle V + m\angle X=180^{\circ}$ and $m\angle W + m\angle V = 180^{\circ}$ from steps 3 and 4.

Step2: Apply subtraction property of equality

Subtract $m\angle V$ from both sides of the equations. Since $m\angle V + m\angle X=m\angle W + m\angle V$, subtracting $m\angle V$ from both sides gives $m\angle X=m\angle W$. The reason for going from $m\angle V + m\angle X=m\angle W + m\angle V$ to $m\angle X=m\angle W$ is the Subtraction Property of Equality (if $a + b=c + b$, then $a=c$).

Answer:

Subtraction Property of Equality