Given:
m || QR
To find:
The measure of ∠QPR.
Solution:
Since m || QR and a transversal line intersect them, therefore the alternate interior angles are equal.
Let points S and T lie on the line m. S is on the right and T is on the left side of point P.
[tex]m\angle RPS=m\angle PRQ[/tex]
[tex]m\angle RPS=45^\circ[/tex]
Now, angles TPQ, QPR and RPS lie on the one side of a straight line. It means, their sum is 180 degrees.
[tex]m\angle TPQ+m\angle QPR+m\angle RPS=180^\circ[/tex]
[tex]50^\circ+m\angle QPR+45^\circ=180^\circ[/tex]
[tex]m\angle QPR+95^\circ=180^\circ[/tex]
[tex]m\angle QPR=180^\circ-95^\circ[/tex]
[tex]m\angle QPR=85^\circ[/tex]
Therefore, the measure of angle QPR is 85 degrees.
