Right angle between 4:30 and 5:00 (repaired): At what time between 4:30 and 5:00 will the hands of a clock be at a right angle?

Introduction / Context:
The original stem said “straight line,” but the options match known right-angle times. Applying the right-angle condition |30H − 5.5M| = 90 with H between 4 and 5 yields two solutions within the hour, one of which lies between 4:30 and 5:00.

Given Data / Assumptions (Recovery Applied):

• Interpretation repaired to “right angle.”
• Hour H = 4; minutes M in (30, 60).
• Equation: |120 − 5.5M| = 90.

Concept / Approach:
Solving yields M = 21 9/11 and M = 54 6/11. Only 54 6/11 is between 4:30 and 5:00.

Step-by-Step Solution:

Verification / Alternative check:
Substitute M = 54 6/11; angle equals 90° exactly.

Why Other Options Are Wrong:
50, 42, 46 minutes are not exact right-angle solutions from the formula.

Common Pitfalls:
Forgetting that the hour hand moves (0.5 deg per minute), hence 5.5M term.

Final Answer:
54 6/11 minutes past 4