The measure of the lesser angle

Geometry Level 2

Find the measure of the obtuse angle determined by the hands of a clock which marks at 10 hours and 20 minutes.

165^\circ

155^\circ

160^\circ

170^\circ

150^\circ

2 solutions

Ashish Menon
Apr 20, 2016

Now, we see that at 20 minutes, deviation of minute hand from mark 12 is $4 × 30 = 120°$

$360°$ rotation of the minute hand gives 1 hour change which is $\dfrac{1}{12} × 360° = 30°$ rotation of hour hand.

So, $120°$ rotation of the minute hand gives 1 hour change which is $\dfrac{30 × 120}{360} = 10°$ rotation of hour hand.

So, the obtuse angle formed between the hour hand and minute hand = $180 - 10 = \boxed{170°}$

Roger Erisman
Apr 13, 2016

Each number on clock is 30 degrees from its neighbors.

Minute hand is 30 degrees times 4 = 120 degrees from 12.

Hour hand is 30 degrees + 40/60 X 30 degrees from 12 = 50 degrees.

Angle is 120 + 50 = 170 degrees.