Question

find the measure of ∠ptu. m∠ptu = °

Explanation:

Step1: Identify angle - relationship

$\angle PTU$ and the angle $(3x + 43)^{\circ}$ are corresponding angles. Since $PQ\parallel RS$, corresponding angles are equal. Also, $\angle PTU$ and $(x + 41)^{\circ}$ are vertical - angles, so $x+41 = 3x + 43$.

Step2: Solve for $x$

\[

$$\begin{align*} x+41&=3x + 43\\ x-3x&=43 - 41\\ -2x&=2\\ x&=- 1 \end{align*}$$

\]

Step3: Find the measure of $\angle PTU$

Substitute $x=-1$ into the expression for $\angle PTU$ (using $x + 41$).
$m\angle PTU=x + 41=(-1)+41 = 40^{\circ}$

Answer:

$40$