m<RST =150, m<GST = x + 131, and m<RSG = x = 41. Find m<GST.

To find the measure of angle GST, we need to use the given information about the angle measures in the triangle.

Let's break down the problem step by step:

1. Start by understanding the given information:
- m<RST = 150 degrees (angle RST measures 150 degrees).
- m<RSG = x = 41 degrees (angle RSG measures 41 degrees).

2. We need to find m<GST, which is the measure of angle GST. We can set up an equation to solve for it.

3. Use the fact that the sum of the angles in a triangle is always 180 degrees. Since we have the measures of angles RST, RSG, and GST, we can write the equation:
m<RST + m<RSG + m<GST = 180 degrees

Substitute the given values:
150 + 41 + m<GST = 180

4. Simplify the equation:
191 + m<GST = 180

5. Subtract 191 from both sides to isolate m<GST:
m<GST = 180 - 191

6. Calculate m<GST:
m<GST = -11 degrees

Therefore, the measure of angle GST (m<GST) is -11 degrees.