Question

find the measure of each angle.

∠qrt = □°

∠trs = □°

Explanation:

Step1: Use the linear - pair property

Since \(\angle QRT\) and \(\angle TRS\) form a linear pair, \(\angle QRT+\angle TRS = 180^{\circ}\).
Given \(\angle QRT=(6x + 4)^{\circ}\) and \(\angle TRS=(6x-28)^{\circ}\), we have the equation \((6x + 4)+(6x-28)=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(6x+4 + 6x-28=180\), which simplifies to \(12x-24 = 180\).
Add \(24\) to both sides: \(12x=180 + 24=204\).
Divide both sides by \(12\): \(x=\frac{204}{12}=17\).

Step3: Find the measure of \(\angle QRT\)

Substitute \(x = 17\) into \(\angle QRT=(6x + 4)^{\circ}\).
\(\angle QRT=6\times17+4=102 + 4=106^{\circ}\).

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

Substitute \(x = 17\) into \(\angle TRS=(6x-28)^{\circ}\).
\(\angle TRS=6\times17-28=102-28 = 74^{\circ}\).

Answer:

\(\angle QRT = 106^{\circ}\), \(\angle TRS=74^{\circ}\)