We are given a diagram where the angles around point T form a straight line. We know that the angle $\angle PTQ$ is 125 degrees and $\angle QTS$ is a right angle, which is 90 degrees. The angle $\angle RTS$ is given as $(5x)$ degrees. The problem asks us to find the value of $x$.

1. Problem Description

We are given a diagram where the angles around point T form a straight line. We know that the angle $\angle PTQ$ is 125 degrees and $\angle QTS$ is a right angle, which is 90 degrees. The angle $\angle RTS$ is given as $(5x)$ degrees. The problem asks us to find the value of $x$.

2. Solution Steps

The angles around point T form a straight line. Therefore, the sum of the angles $\angle PTQ$, $\angle QTS$ and $\angle RTS$ must equal 180 degrees.

$\angle PTQ + \angle QTS + \angle RTS = 180^\circ$

$125^\circ + 90^\circ + (5x)^\circ = 180^\circ$

$215^\circ + 5x^\circ = 180^\circ$

$5x = 180 - 215$

$5x = -35$

$x = \frac{-35}{5}$

$x = -7$

3. Final Answer

-7