Thread: Measure of angle formed by minute and hour hands

Hi,

What is the measure of the angle formed by the minute and hour hands of a clock at 1:50?

(A)
(B)
(C)
(D)
(E)

Answer: D
My guess was after mentally flipping it. My approach was worthless and remains worthless for questions of this type.
I seek a better approach to this question and an explanation of this approach. I ask kindly.

Originally Posted by Hellbent

Hi,

What is the measure of the angle formed by the minute and hour hands of a clock at 1:50?

(A)
(B)
(C)
(D)
(E)

Answer: C
My guess was after mentally flipping it. My approach was worthless and remains worthless for questions of this type.
I seek a better approach to this question and an explanation of this approach. I ask kindly.

A 12-hour clock has 12 subdivisions, each of which is

At 1:50, the minute hand is pointing at 10, so it is left of 12.

The hour hand will have moved of from it's initial position at 1 o'clock, when the minute hand was pointing at 12.

This leaves it to the right of 12.

Originally Posted by Archie Meade

A 12-hour clock has 12 subdivisions, each of which is

At 1:50, the minute hand is pointing at 10, so it is left of 12.

The hour hand will have moved of from it's initial position at 1 o'clock, when the minute hand was pointing at 12.

This leaves it to the right of 12.

My understanding is much better. I am having a problem with this part: The hour hand will have moved of , when the minute hand was pointing at 12.

Wouldn't it have been the minute hand that moved of ? Seeing that it has moved from 12 to 10 - .

Originally Posted by Hellbent

My understanding is much better. I am having a problem with this part: The hour hand will have moved of , when the minute hand was pointing at 12.

Wouldn't it have been the minute hand that moved of ? Seeing that it has moved from 12 to 10 - .

I didn't write the first post too well.

Imagine the time is initially 1 o'clock. The minute hand is at 12 and the hour hand is at 1.
Both hands move and the clock reads 1:50.

Yes, the minute hand will have moved through ten times

while the hour hand will have moved through ten times.

The hour hand moves through for a movement of the minute hand.

I'm getting (D), not (C).

Thanks.

Sorry, typo, it is indeed (D.) .

I just changed the values in this question to check my understanding:
What is the measure of the angle formed by the minute and hour hands of a clock at 3:45?


Then adding another (intervening angle between 9 and 12) gives

Would the approach be the same for non-multiples of 5. Say, 4:47?

Originally Posted by Hellbent

Thanks.

Sorry, typo, it is indeed (D.) .

I just changed the values in this question to check my understanding:
What is the measure of the angle formed by the minute and hour hands of a clock at 3:45?


Then adding another (intervening angle between 9 and 12) gives

Would the approach be the same for non-multiples of 5. Say, 4:47?

Yes,

Starting at 4 o'clock, the minute hand will swing through

Then the hour hand will swing through

You can simply think in terms of "fractions of an hour" and so "fractions of " and "fractions of "

Thanks.