Question

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

Answer 1

The value of angle QXS is;

`m\measuredangle QXS=40^0`

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`

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}`

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}`

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}`

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}`

Therefore, the value of angle QXS is;

`m\measuredangle QXS=40^0`