Question

given: ( mangle qvr = 49^{circ} ) prove: ( x = 15 ) complete the steps of the proof. statements reasons 1. ( mangle qvr = 49 ) 1. given 2. ( mangle uvt = 3x + 4 ) 2. given 3. ( angle qvr ) and ( angle uvt ) are vertical angles. 3. definition of vertical angles 4. ( angle uvtcongangle qvr ) 4. 5. ( mangle uvt = mangle qvr ) 5. definition of congruence 6. 6. substitution property 7. ( 3x = 45 ) 7. subtraction property 8. ( x = 15 ) 8. division property

Explanation:

Step1: Reason for statement 4

Vertical angles are congruent. So, the reason for statement 4 is "vertical angles theorem".

Step2: Statement 6

Since \(m\angle UVT = 3x + 4\) (statement 2) and \(m\angle QVR=49\) (statement 1) and \(m\angle UVT=m\angle QVR\) (statement 5), by substitution property, the statement 6 is \(3x + 4=49\).

Answer:

1. vertical angles theorem; 6. \(3x + 4 = 49\)