In the diagram, you are given two straight lines, $PRT$ and $QRS$, and a few angles. Specifically, you are provided the following information:

1. $\angle PRS = 50^\circ$
2. $\angle QRT = 95^\circ$
3. $\angle RTS = x^\circ$

To solve for $x$, let's apply the following steps:

Step 1: Use the fact that $\angle QRT$ and $\angle SRT$ are supplementary

Since $QRS$ is a straight line, we know that: $\angle QRT + \angle SRT = 180^\circ$ Given that $\angle QRT = 95^\circ$, we can find $\angle SRT$: $95^\circ + \angle SRT = 180^\circ$ $\angle SRT = 180^\circ - 95^\circ = 85^\circ$

Step 2: Use the sum of angles in $\triangle RTS$

In $\triangle RTS$, the sum of the internal angles must be $180^\circ$. Therefore, we have: $\angle RTS + \angle SRT + \angle RST = 180^\circ$ We already know $\angle RTS = x^\circ$ and $\angle SRT = 85^\circ$, and $\angle RST = 50^\circ$ is given. Plugging in these values: $x + 85^\circ + 50^\circ = 180^\circ$ $x + 135^\circ = 180^\circ$ $x = 180^\circ - 135^\circ = 45^\circ$

Thus, the value of $x$ is $\boxed{45^\circ}$.

Final Answer:

The correct answer is $\boxed{B}$.

Would you like further clarification or details on any steps?

Here are 5 related questions to practice:

1. If $\angle QRT$ was 100°, what would $x$ be?
2. How do you calculate exterior angles in triangles?
3. What is the sum of the interior angles of a quadrilateral?
4. In any triangle, how can you determine the third angle if you have two?
5. What are supplementary angles, and how are they applied in straight-line geometry?

Tip: Always remember that the sum of angles in a triangle is $180^\circ$. This rule is fundamental in many geometry problems!