Question

given ( mangle qvr = 49^{circ}) prove ( x = 15) complete the steps of the proof

Explanation:

Step1: Reason for statement 4

Vertical angles theorem states that vertical angles are congruent. Since \(\angle QVR\) and \(\angle UVT\) are vertical angles (statement 3), the reason for \(\angle UVT\cong\angle QVR\) (statement 4) is the vertical angles theorem.

Step2: Statement 6

From statement 2 (\(m\angle UVT = 3x + 4\)) and statement 5 (\(m\angle UVT=m\angle QVR\)) and given \(m\angle QVR = 49\) (statement 1), by substitution property (statement 6 reason), we substitute \(m\angle UVT\) with \(3x + 4\) and \(m\angle QVR\) with \(49\). So the statement is \(3x + 4=49\).

Answer:

1. vertical angles theorem
2. \(3x + 4=49\)