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need helpp pls i don't know how to do it.

Need Helpp Pls I Dont Know How To Do It class=

Sagot :

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]

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