Question

in the diagram, roads a and b are parallel. solve for x and find the measure of ∠vtu. (x + 40)° (2x - 22)° p r v x = m∠vtu =

Explanation:

Step1: Use corresponding - angles property

Since roads \(a\) and \(b\) are parallel, \(\angle QRP\) and \(\angle VTS\) are corresponding angles and are equal. So, \(x + 40=2x-22\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation \(x + 40=2x-22\):
\(40=x - 22\).
Then add 22 to both sides: \(x=40 + 22=62\).

Step3: Find the measure of \(\angle VTU\)

\(\angle VTU\) and \(\angle VTS\) are supplementary (a linear - pair of angles), so \(m\angle VTU=180-(2x - 22)\).
Substitute \(x = 62\) into the expression: \(2x-22=2\times62-22=124 - 22 = 102\).
Then \(m\angle VTU=180 - 102=78\).

Answer:

\(x = 62\)
\(m\angle VTU=78\)