Question

find the measure of ∠ptu.

Explanation:

Step1: Identify angle - relationship

Since $\angle PTU$ and $(2x + 36)^{\circ}$ are corresponding angles (assuming $PQ\parallel RS$), they are equal. Also, $(9x - 20)^{\circ}$ and $(2x+36)^{\circ}$ are vertical - angles, so they are equal.
$9x-20 = 2x + 36$

Step2: Solve for x

Subtract $2x$ from both sides:
$9x-2x-20=2x - 2x+36$
$7x-20 = 36$
Add 20 to both sides:
$7x-20 + 20=36 + 20$
$7x=56$
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 $2x + 36$).
$\angle PTU=2x + 36=2\times8+36$
$=16 + 36=52^{\circ}$

Answer:

$52^{\circ}$