Question

Lines \( l \) and \( m \) are parallel. \( O \) is the center of the circle. The measure of angle \( d \) is \( 45^\circ \). The length of line \( RS \) is \( \frac{\sqrt{2}}{2} \). Line \( RS \) forms a right angle with line \( m \). What is the measure of angle \( a \)?

• A. 45°
• B. 90°
• C. 60°
• D. 30°

Hint:

When dealing with parallel lines and angles, remember that alternate interior angles and supplementary angles play an important role.

Answer 1

The Correct Option is B

Step 1: Analyze the figure.
The lines \( l \) and \( m \) are parallel, and the angle \( d \) is given as 45°. The angle formed by line \( RS \) is a right angle with line \( m \).
Step 2: Conclusion.
Since the two lines are parallel, angle \( a \) is supplementary to angle \( d \), and hence, angle \( a \) must be 90°.