The distance between each notch on the clock is 6 degrees because there are 360 degrees on the clock, and there are 60 notches total. The minute hand is at notch #20, and so it is 120 degrees from the top. The hour hand is a little past notch #40 because the time is a little past hour 8. Thus, the hour hand is a little past 240 degrees from the top, going clockwise ($\displaystyle 40\times 6$ degrees).

In each hour, the hour hand goes 5 notches, or 30 degrees.  Because it is now 20 minutes past the hour, a third of an hour has passed.  One third of 30 degrees is 10 degrees.  Thus, the hour hand is 10 degrees past notch #40.  The hour hand is 250 degrees from the top, going clockwise.  The angle between the two hands is thus 130 degrees.  

This is a proportion problem

 $\displaystyle \frac{12.5}{100}=\frac{x \; degrees}{360\; degrees}$ so there are $\displaystyle 45^{\circ}$ in $\displaystyle 12.5$ percent of a circle

First note that a clock is a circle made of 360 degrees, and that each number represents an angle and the separation between them is 360/12 = 30. And at 2:00, the minute hand is on the 12 and the hour hand is on the 2.  The correct answer is 2 * 30 = 60 degrees.

The interior angle of a sector is equal the the angle of the sector. If the entire circumference was the sector, it would equal $\displaystyle \small 360^o$. Additionally, if it were 12:00, the angle would be equal to $\displaystyle \small 360^o$. We can solve the problem by setting up a proportion. 2:00 will be two-twelfths of the circle past the 12:00 mark, and will be at an angle of $\displaystyle \small x^o$.

$\displaystyle \frac{2}{12}=\frac{x^o}{360^o}$

Cross multiply and solve for $\displaystyle \small x^o$.

$\displaystyle 720^o=12x^o$

$\displaystyle x=60^o$

At four o’clock the minute hand is on the 12 and the hour hand is on the 4.  The angle formed is 4/12 of the total number of degrees in a circle, 360.

4/12 * 360 = 120 degrees

A clock is a circle, and a circle always contains 360 degrees. Since there are 60 minutes on a clock, each minute mark is 6 degrees.

$\displaystyle \frac{360^o\ \text{total}}{60\ \text{minutes total}}=6\ \text{degrees per minute}$

The minute hand on the clock will point at 15 minutes, allowing us to calculate it's position on the circle.

$\displaystyle (15\ min)(6)=90^o$

Since there are 12 hours on the clock, each hour mark is 30 degrees.

$\displaystyle \frac{360^o\ \text{total}}{12\ \text{hours total}}=30\ \text{degrees per hour}$

We can calculate where the hour hand will be at 8:00.

$\displaystyle (8\ hr)(30)=240^o$

However, the hour hand will actually be between the 8 and the 9, since we are looking at 8:15 rather than an absolute hour mark. 15 minutes is equal to one-fourth of an hour. Use the same equation to find the additional position of the hour hand.

$\displaystyle 240^o+(\frac{1}{4}\ hr)(30)$

$\displaystyle 240^o+7.5^o$

$\displaystyle 247.5^o$

We are looking for the angle between the two hands of the clock. The will be equal to the difference between the two angle measures.

$\displaystyle \angle=247.5^o-90^o=157.5^o$

A analog clock is divided up into 12 sectors, based on the numbers 1–12. One sector represents 30 degrees (360/12 = 30). If the hour hand is directly on the 10, and the minute hand is on the 2, that means there are 4 sectors of 30 degrees between then, thus they are 120 degrees apart (30 * 4 = 120).

The entire clock measures 360°. As the clock is divided into 12 sections, the distance between each number is equivalent to 30° (360/12). The distance between the 2 and the 3 on the clock is 30°.  One has to account, however, for the 10 minutes that have passed. 10 minutes is 1/6 of an hour so the hour hand has also moved 1/6 of the distance between the 3 and the 4, which adds 5° (1/6 of 30°). The total measure of the angle, therefore, is 35°.