angle between two lines

Question

what are the angles between hands of a clock at 5 A.M

 

(a)155 & 215 degree

(b)150 & 250 degree

(c)120 &240 degree

(d)150 & 210 degree

Answer 1

The 12 hour markings of the clock are 30° apart.  That's because there are 12 of them, they are evenly spaced, and the total angle around the circle of the clock is 360°.

 

At 5AM, the minute hand points directly at the 12, and the hour hand points directly at the 5.  So the two hands are 5 markings apart, which is 150°.

 

But if you count around the other way, they are 7 markings apart, which is 210°.  (And of course the two angles have to add to 360°.)  So the answer is (d).