Question

complete the proof that ∠vxw≅∠txu.
statement
1 m∠txu + m∠uxv = 180°
2 m∠uxv + m∠vxw = 180°
3 m∠txu + m∠uxv = m∠uxv + m∠vxw
4 m∠txu = m∠vxw
5 ∠vxw≅∠txu
reason

Explanation:

Step1: Adjacent - angle addition

$\angle TXU$ and $\angle UXV$ form a linear - pair. A linear pair of angles is supplementary, so $m\angle TXU + m\angle UXV=180^{\circ}$ (Definition of linear pair).

Step2: Adjacent - angle addition

$\angle UXV$ and $\angle VXW$ form a linear - pair. A linear pair of angles is supplementary, so $m\angle UXV + m\angle VXW = 180^{\circ}$ (Definition of linear pair).

Step3: Substitution property

Since $m\angle TXU + m\angle UXV = 180^{\circ}$ and $m\angle UXV + m\angle VXW = 180^{\circ}$, we can substitute to get $m\angle TXU + m\angle UXV=m\angle UXV + m\angle VXW$.

Step4: Subtraction property of equality

Subtract $m\angle UXV$ from both sides of the equation $m\angle TXU + m\angle UXV=m\angle UXV + m\angle VXW$. We get $m\angle TXU=m\angle VXW$.

Step5: Definition of congruent angles

If two angles have the same measure, they are congruent. So $\angle VXW\cong\angle TXU$.

Answer:

1. Definition of linear pair
2. Definition of linear pair
3. Substitution property
4. Subtraction property of equality
5. Definition of congruent angles