Question

1. m∠pqr

(3n - 45)°
(2n + 15)°

Explanation:

Step1: Use the property of alternate interior angles

Since the two lines are parallel, the alternate interior angles are equal. So, \(2n + 15=3n - 45\).

Step2: Solve the equation for \(n\)

Subtract \(2n\) from both sides: \(15=n - 45\).
Add \(45\) to both sides: \(n = 60\).

Step3: Find \(m\angle PQR\)

Substitute \(n = 60\) into \(2n+15\). \(2\times60 + 15=120 + 15=135\).

Answer:

\(135^{\circ}\)