type 1 angle between the hands of clock Detailed Explanation And More Example

Answer: (c)

Angle traced by the hour hand in 12 hrs = 360°

Angle traced by the hour hand in 5 hrs 10 min, i.e., $31/6 hrs = (360/12 × 31/6)^o = 155°$ 

Answer: (a)

Angle traced by the minute hand in 5 minutes = $(360/60 × 5)^o = 30°$

Answer: (c)

Angle traced by hour hand in 12 hrs = 360°

Angle traced by it in 11/3 hrs = $(360/12 × 11/3)° = 110°$

Angle traced by minute hand in 60 min = 360°

Angle traced by it in 40 min = $(360/60 × 40)^o$ = 240°

∴ Required angle = $(240 - 110)^o$ = 130°

Answer: (d)

Angle traced by hour hand in 35 min after $8 = 35 × 1°/2 = 17.5°$

At 8 : 35, min hand is at 7, and angle between 8 and 7 = 30°

∴ required angle between two hand at 8 : 35 = 30° + 17.5° = 47.5°

Answer: (d)

∴ angle traced by hour hand per minute = $(1/2)^o$

Therefore angle traced by hour hand in 4 h 10 min = $[(4 × 60) + 10] × 1°/2 = 250 × 1°/2 = 125°$

∴ angle traced by minute hand per minute = 6°

∴ angle traced by minute hand in 10 min = 10 × 6° = 60°

∴ required angle = 125° - 60° = 65°

Answer: (b)

Angle traced by minute hand per minute = 6°

Therefore angle traced by minute hand in 12 h 20 min = [(2 × 60) + 20] × 6°

= (120 + 20) × 6° = 140 × 6° = 840°