Question

given: ( mangle qvr = 49^circ )
prove: ( x = 15 )

complete the steps of the proof.

vertical angles theorem
( 3x + 4 = 15 )
( 3x + 4 = 49 )
measure of angle qvr = 49 degrees
measure of angle uvt = ( (3x + 4) ) degrees

Explanation:

Step1: Apply Vertical Angles Theorem

Vertical angles are equal, so \( m\angle QVR = m\angle UVT \). Given \( m\angle QVR = 49^\circ \) and \( m\angle UVT=(3x + 4)^\circ \), we set up the equation:
\( 3x + 4 = 49 \)

Step2: Solve for \( x \)

Subtract 4 from both sides:
\( 3x = 49 - 4 = 45 \)
Divide both sides by 3:
\( x=\frac{45}{3}=15 \)

Answer:

\( x = 15 \) is proven as shown in the steps.