Final answer:
The measure of angle PQR is also 2n degrees.
Step-by-step explanation:
The angle bisector of PQR is QE. Let's find the relationship between mPQE and mPQR. The angle bisector theorem states that the angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the lengths of the other two sides. In other words, if QE is the angle bisector of PQR, then we can say that PE/PQ = EQ/QR.
Since we know that mPQE = 2n degrees, we can plug this value into the angle bisector theorem equation and solve for mPQR. Multiplying both sides of the equation by QR, we get: PE * QR = EQ * PQ. Substituting 2n for mPQE, we have: PE * QR = EQ * PQ = 2n.
Therefore, mPQR = 2n degrees, which means that the measure of angle PQR is also 2n degrees.