Question

∠v and ∠x are complementary and ∠v and ∠w are complementary. complete the proof that ∠x≅∠w. statement reason 1 ∠v and ∠x are complementary given 2 ∠v and ∠w are complementary given 3 m∠v + m∠x = 90° 4 m∠v + m∠w = 90° 5 m∠v + m∠x = m∠v + m∠w 6 m∠x = m∠w properties of addition, subtraction, multiplication, and division definition of congruence 7 ∠x≅∠w

Explanation:

Step1: Recall complementary - angle definition

If two angles are complementary, the sum of their measures is 90°. Since ∠V and ∠X are complementary, $m\angle V + m\angle X=90^{\circ}$.

Step2: Apply complementary - angle definition again

Since ∠V and ∠W are complementary, $m\angle V + m\angle W = 90^{\circ}$.

Step3: Use transitive property of equality

Because $m\angle V + m\angle X=90^{\circ}$ and $m\angle V + m\angle W = 90^{\circ}$, we can say $m\angle V + m\angle X=m\angle V + m\angle W$ (transitive property of equality).

Step4: Subtract m∠V from both sides

Subtracting $m\angle V$ from both sides of the equation $m\angle V + m\angle X=m\angle V + m\angle W$ (using subtraction property of equality), we get $m\angle X=m\angle W$.

Step5: Use congruence definition

By the definition of congruent angles (if two angles have the same measure, they are congruent), since $m\angle X=m\angle W$, then $\angle X\cong\angle W$.

Answer:

1. Definition of complementary angles; 4. Definition of complementary angles; 5. Transitive property of equality; 6. Subtraction property of equality