Clock angle — What is the angle between the minute hand and the hour hand at exactly 11:50 AM?

Introduction / Context:We compute the smaller angle between clock hands at a given time using standard formulas.

Given Data / Assumptions:

• Hour angle = 30*h + 0.5*m.
• Minute angle = 6*m.
• At 11:50 → h = 11, m = 50.

Concept / Approach:Angle difference = |(30h + 0.5m) − 6m|; if needed, use the smaller of the acute/reflex angles.

Step-by-Step Solution:Hour angle = 30*11 + 0.5*50 = 330 + 25 = 355.Minute angle = 6*50 = 300.Difference = |355 − 300| = 55 degrees.

Verification / Alternative check:The reflex angle would be 360 − 55 = 305 degrees; by convention, we report the smaller angle unless stated otherwise.

Why Other Options Are Wrong:22.5° (right angle halved) and 15° do not correspond to 11:50; “None” is wrong because 55° is obtainable.

Common Pitfalls:Forgetting to include the hour hand’s advance due to the 50 minutes elapsed.

Final Answer:55°.