Answer:
The value of angle QXS is;
![m\measuredangle QXS=40^0](https://img.qammunity.org/2023/formulas/mathematics/high-school/wcktt6ug84cx9lq042s8ni4sk6wyitot4t.png)
Step-by-step explanation:
From the given diagram in question 1:
We can see that angle QXT equals the sum of angle SXT and angle QXS;
![m\measuredangle QXT=m\measuredangle SXT+m\measuredangle QXS](https://img.qammunity.org/2023/formulas/mathematics/high-school/owyc2aplatww4vd9ht9wjrsecxon2kg2dq.png)
Given in the question is the value of angle SXT and angle QXS;
![\begin{gathered} m\measuredangle SXT=4x+1 \\ m\measuredangle QXS=2x-2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/h61121wzzbo3yoqax5esho61jwah1kayoh.png)
Substituting the values into the equation above;
![\begin{gathered} m\measuredangle QXT=m\measuredangle SXT+m\measuredangle QXS \\ m\measuredangle QXT=4x+1+2x-2 \\ m\measuredangle QXT=4x+2x+1-2 \\ m\measuredangle QXT=6x-1 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/dqmwnccqkq4raujtnc31phbuskm5rsg73u.png)
Since angle QXT is equal to 125 degree, then;
![\begin{gathered} m\measuredangle QXT=6x-1=125 \\ 6x-1=125 \\ 6x=125+1 \\ 6x=126 \\ (6x)/(6)=(126)/(6) \\ x=21 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/8fb11dvhr1m7hit757ll06rmziwyazkzxd.png)
We can now substitute the value of x to get the value of angle QXS;
![\begin{gathered} m\measuredangle QXS=2x-2 \\ m\measuredangle QXS=2(21)-2 \\ m\measuredangle QXS=42-2 \\ m\measuredangle QXS=40^0 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/syzvjqu3wjtkscqklnqvi6mqgp7gs26899.png)
Therefore, the value of angle QXS is;
![m\measuredangle QXS=40^0](https://img.qammunity.org/2023/formulas/mathematics/high-school/wcktt6ug84cx9lq042s8ni4sk6wyitot4t.png)