Question

if m∠prq = m∠prs = 44°, pq = 3v, and ps = v + 40, what is the value of v?

Explanation:

Step1: Identify congruent triangles

Since $\angle PRQ=\angle PRS = 44^{\circ}$, $\angle Q=\angle S = 90^{\circ}$ and $PR$ is common to both $\triangle PQR$ and $\triangle PSR$, by the Angle - Angle - Side (AAS) congruence criterion, $\triangle PQR\cong\triangle PSR$.

Step2: Set up equation from congruent - side property

For congruent triangles, corresponding sides are equal. So, $PQ = PS$. Given $PQ = 3v$ and $PS=v + 40$, we have the equation $3v=v + 40$.

Step3: Solve the equation for v

Subtract $v$ from both sides: $3v−v=v + 40−v$, which simplifies to $2v=40$. Then divide both sides by 2: $\frac{2v}{2}=\frac{40}{2}$, so $v = 20$.

Answer:

$20$