Question

in the diagram below of triangle rst, u is the midpoint of $overline{rt}$ and v is the midpoint of $overline{st}$. if m$angle tsr=-5x + 93$, and m$angle tvu = 82+6x$, what is the measure of $angle tsr$?

Explanation:

Step1: Apply mid - point theorem

Since \(U\) is the mid - point of \(\overline{RT}\) and \(V\) is the mid - point of \(\overline{ST}\), by the mid - point theorem, \(UV\parallel SR\). Then \(\angle TVU=\angle TSR\) (corresponding angles).

Step2: Set up the equation

Set \(-5x + 93=82 + 6x\).

Step3: Solve for \(x\)

Add \(5x\) to both sides: \(93=82 + 6x+5x\), which simplifies to \(93=82 + 11x\). Then subtract 82 from both sides: \(11x=93 - 82=11\). Divide both sides by 11, so \(x = 1\).

Step4: Find the measure of \(\angle TSR\)

Substitute \(x = 1\) into the expression for \(\angle TSR\): \(\angle TSR=-5(1)+93=-5 + 93=88\).

Answer:

88