Clock Angle At Rush Hour

Each $\color{#3D99F6}5~minute$ mark subtends an angle of $\color{#3D99F6}30^\circ$ from the center of the clock (see left photo).

In the $\color{#3D99F6}5~o'clock$ position (see right photo), there are $\color{#3D99F6}5-$ $\color{#3D99F6}5~minute$ marks. Therefore, $x=5(30)=$ $\color{#D61F06}\large \boxed{150^\circ}$ .

Using mathematical skills : A circle has 360 degrees, which is the number of degrees that hour hand moves in 12 hours. Hence, the number of degrees that it moves in one hour is 360 / 12 = 30. Since it has moved 5 hours, the angle is 30 * 5 = 150.

Using common sense : According to the answer options, x = 36 or 72 or 150 or 210. And as we all can see that x = an obtuse angle, and so it can only be 150.

In a clock, the angle between each hour is 360/12 = 30. Hence, at 5 o'clock, the angle will be 5 * 30 = 150.

I solved this by Ratio and Proportion. We know that $30$ $minutes$ $=180$ $degrees$ .

Let $x$ be the angle formed

From the figure,

$\frac{x}{25}$ $=$ $\frac{180}{30}$

$x=150$ $degrees$

the hour minuit angle is 30 because 360/12=30

$5~o'clock=(6-1)~o'clock=6~o'clock-1~o'clock$ .We see that $6~o'clock$ is $180^\circ$ . $1~o'clock$ equals $\frac{360}{12} \times 1=30^\circ$ . $\large 180-30=\color{#3D99F6}\large \boxed{150^\circ}$

The hour hand moves $0.5^\circ$ per minute. At $5:00$ , the hour hand moved $5(60)=300$ minutes or $300(0.5^\circ)=150^\circ$ . Since the minute hand is at number $12$ , it did not moved. So the value of $x$ is $150-0=150^\circ$

By looking we can easily judge, It is more then 90 degree and less than 180 degree so the answer is 150 degrees

Assuming a standard analog clock, 90 degrees has 3 1-hour divisions, for example, 1, 2, and 3. 90/3 = 30. So each hour division is 30 degrees. Therefore 5 divisions (between 12 and 5) is 30 * 5 = 150 degrees.

I just used the process of elimination. The angle was more than 90°, but less than 180°. So the only answer within reason was 150°

I used proportions so...

$\frac{6}{180}$ = $\frac{5}{x}$

I used 6 because at 6 o'clock, the angle measure is 180 degrees so I knew that would be proportional to 5 o'clock because there are equal degree differences between each number or every five minutes. If you try to solve for x...

Multiply the denominator of the first fraction by the numerator of the second fraction: 180 * 5 = 900

Divide your answer by the numerator of the first numerator: 900/6 = 150

If x = 150, that means that the angle measure of the clock is 150 degrees.

60 minute = 360 degree. 1 minute = 360/60 = 6degree, When Minute hand in 1 and hour hand in 5, degree = 25 x 6 = 150 degree.

two opposite rays form an angle of 180. also, when 180 degrees is divided by six (there are six parts -- 12 to 6), each gives us 30 degrees. so 12 to 5 = 30*5=150

If 90 degree equals 3 o' clock then , 3:90=5:x, 3x=90*5, 3x=450, 3x/3=450/3 so x equals 150 degree

everyone knows that the straight line's angel is 180 so the line between 12 o'clock and 6 o'clock is 180 degree and there are 6 hours between them so 180/6 =30 and since it is 5 o'clock then 5x30=150

circle = 360 degrees so, there are 12 numbers so divided 360 with 12 = 360 : 12 = 30 it's 5 o'clock. so 30 x 5 = 150 degrees

or 5/12 x 360 = 150 degrees

Every 5 minutes of angle 30 degree , so x=5 (30 degree) =150 degree , hence x=150 degree .

5/12 x 360° = 150°

The clock is a circle, which have $360°$ , if you can't divide 360 by 12 then you can divide 180 by 6, both's result is 30, then you multiply $(30*50)$ and you get 150.

The angle at 3 o clock is 90° so 90/3=30 so each number on a clock is 30°greater then the previous number.

5/6 of 180 degrees is 150

Its a simple approach... 12 is the highest number. Divide by 360.360/12. =30 As it is asking for 5.. 30×5=150.

(360/12)×5=x

1 minute corresponds to 6 degrees. Therefore, 25 minutes corresponds to 150 degrees.

$Total\quad angles\quad in\quad one\quad circle\quad =\quad { 360 }^{ o }\quad =\quad 2\pi \\ Total\quad angles\quad in\quad Clock\quad =\quad \frac { 2\pi }{ 12 } \\ \qquad At\quad 5'o\quad clock\quad angles\quad should\quad be\\ \qquad \qquad =\quad \frac { 2\pi }{ 12 } \times 5\quad =\quad \frac { 5\pi }{ 6 } rad\\ In\quad degree\quad =\quad { 150 }^{ o }$

when the clock is 6 the angel is 180 so the 5 mins angel is 30 180 - 30 =150

every 5 minutes is equal to 30 degrees

360/12=30, 30x5=150

5min=360/12=30=>25min=30*5=150

There is 360 for 60 minutes. So 25 minutes has (360/60)*25=150

we know that the clock is round, like as a circle and circle has 360 degrees, and clock has 60 minutes or 60 equal graduations. So the one minute or one graduation is 360/60=6 . The answer is 6 degree. The hour hand is travelling from 12 to 5 which is equal to 25 minutes or 25 equal graduations, so the degrees at 5 o'clock 25*6=150. The answer is 150 degrees