Question

find the measure of ∠tus. m∠tus =

Explanation:

Step1: Identify angle - relationship

Assume \(PQ\parallel RS\), then \((55 - x)^{\circ}\) and \((63 - 3x)^{\circ}\) are corresponding angles, so \(55 - x=63 - 3x\).

Step2: Solve the equation for \(x\)

Add \(3x\) to both sides: \(55 - x+3x=63 - 3x+3x\), which simplifies to \(55 + 2x=63\). Then subtract 55 from both sides: \(2x=63 - 55\), so \(2x = 8\), and \(x = 4\).

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

Substitute \(x = 4\) into the expression for \(\angle TUS=(63 - 3x)^{\circ}\). Then \(\angle TUS=63-3\times4=63 - 12=51^{\circ}\).

Answer:

\(51\)