Question

problem 14: (first taught in lesson 23) given ℓ || m, find m∠qpr. after you enter your answer press go. m∠qpr =

Explanation:

Step1: Find the interior - angle at R

The exterior angle at R is $120^{\circ}$. The interior - angle at R, say $\angle PRQ$, and the exterior angle at R are supplementary. So $\angle PRQ=180 - 120=60^{\circ}$.

Step2: Use the angle - sum property of a triangle

In $\triangle PQR$, we know one angle $\angle PQR = 30^{\circ}$ and $\angle PRQ = 60^{\circ}$. By the angle - sum property of a triangle ($\angle PQR+\angle QPR+\angle PRQ = 180^{\circ}$), we can find $\angle QPR$. Let $\angle QPR=x$. Then $30 + x+60=180$. Solving for $x$, we get $x=180-(30 + 60)=90^{\circ}$.

Answer:

$90^{\circ}$