Question

points p, q, and s are collinear. what is m∠pqr? m∠pqr =

Explanation:

Step1: Use linear - pair property

Since points $P$, $Q$, and $S$ are collinear, $\angle PQR$ and $\angle RQS$ form a linear - pair. The sum of the measures of angles in a linear - pair is $180^{\circ}$. So, $(3x - 5)+(x + 1)=180$.

Step2: Solve the equation for $x$

Combine like terms: $3x+x-5 + 1=180$, which simplifies to $4x-4 = 180$. Add 4 to both sides: $4x=180 + 4=184$. Then divide both sides by 4: $x=\frac{184}{4}=46$.

Step3: Find the measure of $\angle PQR$

Substitute $x = 46$ into the expression for $\angle PQR$, which is $3x-5$. So, $m\angle PQR=3\times46-5=138 - 5=133^{\circ}$.

Answer:

$133^{\circ}$