Question

∠rqt is a straight angle. what are m∠rqs and m∠tqs? m∠rqs = (square^{circ}) m∠tqs = (square^{circ})

Explanation:

Step1: Set up the equation

Since $\angle RQT$ is a straight - angle and $\angle RQT=\angle RQS+\angle TQS$, we have $(12x + 5)+(9x + 7)=180$.

Step2: Combine like terms

Combining the $x$ terms and the constant terms on the left - hand side, we get $12x+9x+5 + 7=180$, which simplifies to $21x+12 = 180$.

Step3: Solve for $x$

Subtract 12 from both sides of the equation: $21x=180 - 12=168$. Then divide both sides by 21: $x=\frac{168}{21}=8$.

Step4: Find $\angle RQS$

Substitute $x = 8$ into the expression for $\angle RQS$: $\angle RQS=12x + 5=12\times8+5=96 + 5=101^{\circ}$.

Step5: Find $\angle TQS$

Substitute $x = 8$ into the expression for $\angle TQS$: $\angle TQS=9x + 7=9\times8+7=72 + 7=79^{\circ}$.

Answer:

$m\angle RQS = 101^{\circ}$
$m\angle TQS = 79^{\circ}$