Question

find the measure of ∠ptu.
(9x - 20)°
(2x + 36)°
m∠ptu = □°

Explanation:

Step1: Identify angle - relationship

Since \(\angle PTU\) and \((2x + 36)^{\circ}\) are corresponding angles (assuming \(PQ\parallel RS\) as indicated by the arrow - heads), they are congruent. Also, \((9x-20)^{\circ}\) and \((2x + 36)^{\circ}\) are corresponding angles, so \(9x-20=2x + 36\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(9x-2x-20=2x-2x + 36\), which simplifies to \(7x-20 = 36\). Then add 20 to both sides: \(7x-20 + 20=36 + 20\), getting \(7x=56\). Divide both sides by 7: \(x=\frac{56}{7}=8\).

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

Substitute \(x = 8\) into the expression for \(\angle PTU\) (which is equal to \(2x + 36\)). So \(m\angle PTU=2\times8+36\). First, calculate \(2\times8 = 16\), then \(16+36=52\).

Answer:

\(52\)