Question

This is called angle relationships and with triangles. Please help

Answer 1

$\begin{gathered} x=6 \\ m\angle STW=91^{\circ} \end{gathered}$

1) Note that there is a theorem of the External Angle that states its measure is equal to the sum of two remote angles inside a triangle.

2) So, we can write out the following equation and solve it for x:

$\begin{gathered} 14x+17=44+9x+3 \\ 14x-9x=44+3-17 \\ 5x=47-17 \\ 5x=30 \\ \frac{5x}{5}=\frac{30}{5} \\ x=6 \end{gathered}$

Now, we can plug into the expression that states the measure of angle ∠STW and find out the unknown measure:

$\begin{gathered} m\angle STW=14x+7,m\angle STW=14(6)+7=91^{\circ} \\ \end{gathered}$

Thus, this is the answer.