Question

1. identify the angle relationship. solve for x. find the m∠pqr and m∠tqr. the angle relationship represented is x= m∠pqr= m∠tqr= (7x + 3)° (2x + 15)° p q t r

Explanation:

Step1: Identify angle - relationship

The angles $\angle PQR$ and $\angle TQR$ are supplementary, so $(7x + 3)+(2x+15)=180$.

Step2: Combine like - terms

$7x+2x+3 + 15=180$, which simplifies to $9x+18 = 180$.

Step3: Isolate the variable term

Subtract 18 from both sides: $9x=180 - 18$, so $9x=162$.

Step4: Solve for x

Divide both sides by 9: $x=\frac{162}{9}=18$.

Step5: Find $m\angle PQR$

Substitute $x = 18$ into the expression for $\angle PQR$: $m\angle PQR=7x + 3=7\times18+3=126 + 3=129^{\circ}$.

Step6: Find $m\angle TQR$

Substitute $x = 18$ into the expression for $\angle TQR$: $m\angle TQR=2x+15=2\times18+15=36 + 15=51^{\circ}$.

Answer:

The angle relationship represented is supplementary.
$x = 18$,
$m\angle PQR=129^{\circ}$,
$m\angle TQR=51^{\circ}$