Question

The smaller angle between the hands of a clock at $12:25$p.m is:

• A. ${132}^0{30}^{\prime }$
• B. ${137}^0{30}^{\prime }$
• C. ${150}^0$
• D. ${137}^0{32}^{\prime }$

Answer 1

The correct option is B ${137}^0{30}^{\prime }$

Hour hand points to B.

Minute hand points to C.

$60min=360°$ (For minute hand)

$⟹1min=6°⟹25min=150°\therefore \angle AOC=150°$

$12hr=360°$ (For hour hand)

$⟹25min=\frac{360}{12\times 60}\times 25=12°{30}^{\prime }\therefore \angle AOB=12°{30}^{\prime }\angle BOC=\angle AOC-\angle AOB=137°{30}^{\prime }$