Question

given: $m\angle qvr = 49^\circ$
prove: $x = 15$

complete the steps of the proof.

statements

reasons

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1. $m\angle qvr = 49$

1. given

2. $m\angle uvt = 3x + 4$

2. given

3. $\angle qvr$ and $\angle uvt$ are vertical angles.

3. definition of vertical angles

4. $\angle uvt \cong \angle qvr$

4. ♠

5. $m\angle uvt = m\angle qvr$

5. definition of congruence

6. ♦

6. substitution property

7. $3x = 45$

7. subtraction property

8. $x = 15$

8. division property

Explanation:

Step1: Identify reason for congruence

Vertical angles are congruent.

Step2: Substitute angle measures

Substitute $m\angle UVT = 3x+4$ and $m\angle QVR = 49$ into the congruence equation.
<Expression>$3x + 4 = 49$</Expression>

Answer:

For the ♦ (step 4 reason): vertical angles are congruent
For the ◆ (step 6 statement): $3x + 4 = 49$