Time Angle
Clock face 360°; angles at 3, 6, 9 o'clock.
Time Angle
Clock Angle Problems
What you'll learn
- A clock face is a 360° circle.
- Each hour mark spans 30° (360 ÷ 12).
- Find angles at 3, 6, 9, 12 o'clock.
- Intro to angle between hour and minute hands (simple times).
Key concepts
Level 1 — Full circle
Clock face = 360°. 12 hour marks → 360 ÷ 12 = 30° per hour.
Level 2 — Simple times
| Time | Angle between hands |
|---|---|
| 3:00 | 90° (right angle) |
| 6:00 | 180° (straight) |
| 9:00 | 90° |
| 12:00 | 0° (overlap) |
Level 3 — Quarter turns
From 12 to 3 = quarter of 360° = 90°.
Level 4 — Indian context
School assembly at 8 a.m. — compare clock angle to lunch bell at 12 — hands overlap at noon.
NCERT anchor: CBSE Class 4 reasoning; Math-Magic 4 Ch 4 — Tick-Tick-Tick (clock and angles)
Worked example
What angle at 3 o'clock?
Step 1 — Hour at 12, minute at 3.
Step 2 — Quarter turn = 90°.
Answer: **90°**
At 6 o'clock, what angle?
Step 1 — Hands opposite.
Step 2 — Half circle = 180°.
Answer: **180°** (straight angle)
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| 6 o'clock is 90° | Confusing 3 and 6 | 6:00 → 180°, not 90° |
| Each minute mark is 30° | Mixing hour and minute spacing | Hour marks 30° apart; minute marks 6° apart |
| 12:00 is 90° | Overlap at noon | 12:00 → 0° (hands together) |
| Angle can exceed 180° at Class 4 level | Taking reflex angle | Take the smaller angle unless asked otherwise |
Quick check
- Angle at 9:00?
- Degrees in full clock face?
- Angle from 12 to 6?
- Stretch: At 12:30, hour hand has moved halfway toward 1. Is the angle still 0°? (No — intro: small angle opens)
Revision tip: Draw a clock, shade 90° and 180° — link to 3 o'clock and 6 o'clock.
Open the Practice tab for graded questions on Clock Angle Problems.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
Master this topic with Drishti OS
Get unlimited mock tests, AI-powered mentorship, and complete video courses when you join.
Start Free Practice