Answer:
The value of angle QXS is;
[tex]m\measuredangle QXS=40^0[/tex]
Explanation:
From the given diagram in question 1:
We can see that angle QXT equals the sum of angle SXT and angle QXS;
[tex]m\measuredangle QXT=m\measuredangle SXT+m\measuredangle QXS[/tex]
Given in the question is the value of angle SXT and angle QXS;
[tex]\begin{gathered} m\measuredangle SXT=4x+1 \\ m\measuredangle QXS=2x-2 \end{gathered}[/tex]
Substituting the values into the equation above;
[tex]\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}[/tex]
Since angle QXT is equal to 125 degree, then;
[tex]\begin{gathered} m\measuredangle QXT=6x-1=125 \\ 6x-1=125 \\ 6x=125+1 \\ 6x=126 \\ \frac{6x}{6}=\frac{126}{6} \\ x=21 \end{gathered}[/tex]
We can now substitute the value of x to get the value of angle QXS;
[tex]\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}[/tex]
Therefore, the value of angle QXS is;
[tex]m\measuredangle QXS=40^0[/tex]
