Question

find the measure of ∠ptu.
m∠ptu = □°

Explanation:

Step1: Use the property of alternate exterior angles

Since the lines \( RS\parallel PQ\), \( \angle RUO=\angle PTU\) (alternate - exterior angles). And \( \angle RUO=(3x + 43)^{\circ}\), \( \angle PTU=(x + 41)^{\circ}\). Also, \( \angle RUO+\angle PTU = 180^{\circ}\) (linear - pair of angles formed by a transversal intersecting two parallel lines). So, \(3x + 43+x + 41=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(4x+84 = 180\).
Subtract 84 from both sides: \(4x=180 - 84\), so \(4x = 96\).
Divide both sides by 4: \(x=\frac{96}{4}=24\).

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

Substitute \(x = 24\) into the expression for \( \angle PTU\). \(m\angle PTU=(x + 41)^{\circ}\).
\(m\angle PTU=(24 + 41)^{\circ}\).

Answer:

\(65\)