Question

30 multiple choice 5 points q||m what is the measure of ∠3? 115 degrees 110 degrees 25 degrees 65 degrees

Explanation:

Step1: Identify vertical - angle relationship

$\angle2$ and the angle adjacent to the $115^{\circ}$ angle are vertical angles. So $\angle2 = 115^{\circ}$.

Step2: Use the property of parallel lines

Since $q\parallel m$, $\angle2$ and $\angle3$ are same - side interior angles. The sum of same - side interior angles of two parallel lines is $180^{\circ}$.

Step3: Calculate $\angle3$

Let $\angle3=x$. Then $x + 115^{\circ}=180^{\circ}$, so $x=180^{\circ}- 115^{\circ}=65^{\circ}$.

Answer:

65 degrees