Question

May you help me find the M

Answer 1

Notice that the figure on the picture is an isosceles trapezoid, then, the base angles are equal and we would have the following expression:

`9x-17=4x+28`

solving for x, we get:

`\begin{gathered} 9x-17=4x+28 \\ \Rightarrow9x-4x=28+17=45 \\ \Rightarrow5x=45 \\ \Rightarrow x=(45)/(5)=9 \\ x=9 \end{gathered}`

now that we know the value of x, we can find the explicit value of angle Q:

`\begin{gathered} \measuredangle Q=9(5)-17=45-17=28 \\ \Rightarrow\measuredangle Q=28 \end{gathered}`

next, we know as a general rule that the angles in a trapezoid that are adjacent are supplementary, then, we have the following:

`\begin{gathered} \measuredangle Q+\measuredangle T=180 \\ \Rightarrow28+\measuredangle T=180 \\ \Rightarrow\measuredangle T=180-28=152 \\ \measuredangle T=152 \end{gathered}`

therefore, the measure of angle T is 152 degrees