Question

what is m∠pts? enter your answer in the box.

Explanation:

Step1: Set up equation

Since $\angle PTS$ and $\angle RTQ$ are vertical - angles, they are equal. So we set up the equation $11(y - 10)=4y-5$.

Step2: Expand left - hand side

Expand $11(y - 10)$ to get $11y-110 = 4y - 5$.

Step3: Move terms with y to one side

Subtract $4y$ from both sides: $11y-4y-110=4y - 4y-5$, which simplifies to $7y-110=-5$.

Step4: Move constant to the other side

Add 110 to both sides: $7y-110 + 110=-5 + 110$, so $7y = 105$.

Step5: Solve for y

Divide both sides by 7: $y=\frac{105}{7}=15$.

Step6: Find the measure of $\angle PTS$

Substitute $y = 15$ into the expression for $\angle PTS$ which is $11(y - 10)$. So $11\times(15 - 10)=11\times5 = 55$.

Answer:

$55$