Question

In the following figure, m || QR. Then, the measure of ∠QPR is

Answer 1

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.

$m\angle RPS=m\angle PRQ$

$m\angle RPS=45^\circ$

Now, angles TPQ, QPR and RPS lie on the one side of a straight line. It means, their sum is 180 degrees.

$m\angle TPQ+m\angle QPR+m\angle RPS=180^\circ$

$50^\circ+m\angle QPR+45^\circ=180^\circ$

$m\angle QPR+95^\circ=180^\circ$

$m\angle QPR=180^\circ-95^\circ$

$m\angle QPR=85^\circ$

Therefore, the measure of angle QPR is 85 degrees.