Question

1. point r is in the interior of ∠qps, ∠qpr ≅ ∠rps. if m∠qpr=(x + 12)° and m∠rps=(2x)°, what is the m∠qps?

Explanation:

Step1: Set up the equation

Since $\angle QPR\cong\angle RPS$, we have $x + 12=2x$.

Step2: Solve for $x$

Subtract $x$ from both sides of the equation $x + 12=2x$. We get $12=2x - x$, so $x = 12$.

Step3: Find the measure of $\angle QPR$ and $\angle RPS$

Substitute $x = 12$ into the expressions for the angles. $m\angle QPR=x + 12=12+12 = 24^{\circ}$ and $m\angle RPS=2x=2\times12 = 24^{\circ}$.

Step4: Find the measure of $\angle QPS$

Since $\angle QPS=\angle QPR+\angle RPS$, then $m\angle QPS=24^{\circ}+24^{\circ}=48^{\circ}$.

Answer:

$48^{\circ}$