Question

given: m∠qvr = 49° prove: x = 15 complete the steps of the proof. statements reasons 1. m∠qvr = 49 1. given 2. m∠uvt = 3x + 4 2. given 3. ∠qvr and ∠uvt are vertical angles. 3. definition of vertical angles 4. ∠uvt ≅ ∠qvr 4. 5. m∠uvt = m∠qvr 5. definition of congruence 6. 6. substitution property 7. 3x = 45 7. subtraction property 8. x = 15 8. division property

Explanation:

Step1: Recall vertical - angles property

Vertical angles are congruent. Since $\angle QVR$ and $\angle UVT$ are vertical angles, if two angles are congruent, their measures are equal. So the reason for step 4 is "vertical angles are congruent".

Step2: Substitute angle measures

We know that $m\angle QVR = 49$ and $m\angle UVT=3x + 4$. By the substitution property, we set up the equation $3x + 4=49$. So the statement for step 6 is $3x + 4=49$.

Answer:

1. vertical angles are congruent
2. $3x + 4 = 49$