Question

what is m∠pqr? m∠pqr =

Explanation:

Step1: Set up equation

Since $\angle PQR$ and $\angle RQS$ are a linear - pair and the sum of angles in a linear - pair is $180^{\circ}$, we have $(3x + 5)+(x + 3)=180$.

Step2: Combine like terms

Combine the $x$ terms and the constant terms: $3x+x+5 + 3=180$, which simplifies to $4x+8 = 180$.

Step3: Solve for $x$

Subtract 8 from both sides: $4x=180 - 8=172$. Then divide both sides by 4: $x=\frac{172}{4}=43$.

Step4: Find $m\angle PQR$

Substitute $x = 43$ into the expression for $\angle PQR$ which is $3x + 5$. So $m\angle PQR=3\times43+5=129 + 5=134^{\circ}$.

Answer:

$134$