Question

∠rqt is a straight angle. what are m∠rqs and m∠tqs? m∠rqs =

Explanation:

1. First, use the fact that a straight - angle has a measure of 180°.

• Since \(\angle RQT\) is a straight angle and \(\angle RQS=(11x + 7)^{\circ}\) and \(\angle TQS=(8x + 2)^{\circ}\), we know that \(\angle RQS+\angle TQS=\angle RQT = 180^{\circ}\).
• So, \((11x + 7)+(8x + 2)=180\).
• Combine like - terms: \(11x+8x+7 + 2=180\), which simplifies to \(19x+9 = 180\).
• Subtract 9 from both sides: \(19x=180 - 9=171\).
• Divide both sides by 19: \(x=\frac{171}{19}=9\).

1. Then, find the measure of \(\angle RQS\):

• Substitute \(x = 9\) into the expression for \(\angle RQS\).
• \(\angle RQS=(11x + 7)^{\circ}\), so \(\angle RQS=11\times9 + 7=99 + 7=106^{\circ}\).

1. Next, find the measure of \(\angle TQS\):

• Substitute \(x = 9\) into the expression for \(\angle TQS\).
• \(\angle TQS=(8x + 2)^{\circ}\), so \(\angle TQS=8\times9+2=72 + 2=74^{\circ}\).

Answer:

\(m\angle RQS = 106^{\circ}\), \(m\angle TQS = 74^{\circ}\)