Notice that the figure on the picture is an isosceles trapezoid, then, the base angles are equal and we would have the following expression:
[tex]9x-17=4x+28[/tex]
solving for x, we get:
[tex]\begin{gathered} 9x-17=4x+28 \\ \Rightarrow9x-4x=28+17=45 \\ \Rightarrow5x=45 \\ \Rightarrow x=\frac{45}{5}=9 \\ x=9 \end{gathered}[/tex]
now that we know the value of x, we can find the explicit value of angle Q:
[tex]\begin{gathered} \measuredangle Q=9(5)-17=45-17=28 \\ \Rightarrow\measuredangle Q=28 \end{gathered}[/tex]
next, we know as a general rule that the angles in a trapezoid that are adjacent are supplementary, then, we have the following:
[tex]\begin{gathered} \measuredangle Q+\measuredangle T=180 \\ \Rightarrow28+\measuredangle T=180 \\ \Rightarrow\measuredangle T=180-28=152 \\ \measuredangle T=152 \end{gathered}[/tex]
therefore, the measure of angle T is 152 degrees
