Question

∠v and ∠x are supplementary and ∠w and ∠v are supplementary. complete the proof that ∠x≅∠w. statement reason 1 ∠v and ∠x are supplementary given 2 ∠w and ∠v are supplementary given 3 m∠v + m∠x = 180° definition of supplementary angles 4 m∠w + m∠v = 180° definition of supplementary angles 5 m∠v + m∠x = m∠w + m∠v transitive property of equality 6 m∠x = m∠w reflexive property of equality 7 ∠x≅∠w definition of congruence

Explanation:

Step1: Recall supplementary - angle definition

Since $\angle V$ and $\angle X$ are supplementary, $m\angle V + m\angle X=180^{\circ}$ by the definition of supplementary angles.

Step2: Apply definition again

Since $\angle W$ and $\angle V$ are supplementary, $m\angle W + m\angle V = 180^{\circ}$ by the definition of supplementary angles.

Step3: Use transitive property

By the transitive property of equality, if $a = c$ and $b = c$, then $a = b$. Here, $m\angle V + m\angle X=m\angle W + m\angle V$ because both equal $180^{\circ}$.

Step4: Subtract $m\angle V$ from both sides

Subtracting $m\angle V$ from both sides of the equation $m\angle V + m\angle X=m\angle W + m\angle V$, we get $m\angle X=m\angle W$ (Subtraction Property of Equality, not reflexive as in the original incorrect - step 6).

Step5: Use congruence definition

By the definition of congruence (if two angles have equal measures, they are congruent), $\angle X\cong\angle W$.

Answer:

The proof is completed as above to show $\angle X\cong\angle W$. The corrected reason for step 6 should be the Subtraction Property of Equality.