Use the conversion \(\displaystyle \pi \textup{ radians}= 180\textup{ degrees}\).

Since we are converting radians to degrees, multiply by 180 degrees and divide by \(\displaystyle \pi\) radians.

\(\displaystyle \frac{2\pi}{3} \textup{ radians}\left(\frac{180 \textup{ degrees}}{\pi\textup{ radian}}\right)= 120\textup{ degrees}\)

When going from radians to degrees one multiplies by the conversion factor 

\(\displaystyle \frac{180^{\circ}}{\pi rad}\).

The radians cancel and the answer is left in degrees.

\(\displaystyle 3\hspace{1mm}{\color{Red} rad}\cdot\frac{180^{\circ}}{\pi {\color{Red} rad}}=\frac{540^\circ}{\pi}=172^{\circ}\)

To convert to radians, set up the ratio \(\displaystyle \frac{180}{\pi } = \frac{33} { x}\):

\(\displaystyle 180 x = 33 \pi\)

\(\displaystyle x = 33 \pi \div 180 \approx 0.576\)

To convert, divide by \(\displaystyle \pi\) and multiply by \(\displaystyle 180\):

\(\displaystyle \frac{2 \pi }{7 } \div \pi = \frac{2}{7}\)

\(\displaystyle \frac{2}{7} \cdot 180 \approx 51.47^o\)

Recall the definition of "radians" derived from the unit circle:

\(\displaystyle 180^{\circ} = \pi rad\)

The quantity of radians given in the problem is \(\displaystyle \frac{7\pi}{4}\). All that is required to convert this measure into degrees is to denote the unknown angle measure in degrees by \(\displaystyle \Theta\) and set up a proportion equation using the aforementioned definition relating radians to degrees:

\(\displaystyle \frac{180^{\circ}}{\Theta} = \frac{\pi rad}{\frac{7\pi}{4} rad}\)

Cross-multiply the denominators in these fractions to obtain:

\(\displaystyle 1260^{\circ}\pi rad=4\Theta\pi rad\)

or

\(\displaystyle 315^{\circ}\pi rad =\Theta\pi rad\).

Canceling like terms in these equations yields

\(\displaystyle \Theta = 315^{\circ}\)

Hence, the correct angle measure of \(\displaystyle \frac{7\pi}{4}\) in degrees is \(\displaystyle 315^{\circ}\).

1 radian is equal to \(\displaystyle \frac{180}{\pi}\) degrees. Using this conversion factor,

\(\displaystyle \frac{37\pi}{18}\times\frac{180}{\pi}=37\times10=370\).

Recall that there are 360 degrees in a circle which is equivalent to \(\displaystyle 2\pi\) radians. In order to convert between radians and degrees use the relationship that,

\(\displaystyle 360^\circ=2\pi \Rightarrow 180^\circ=\pi\)

Thus, in order to convert from degrees to radians you need to multiply by \(\displaystyle \frac{\pi}{180}\).

So in this particular case, 

\(\displaystyle 150*\frac{\pi}{180}=\frac{5\pi}{6}\).

Recall that there are 360 degrees in a circle which is equivalent to  radians. In order to convert between radians and degrees use the relationship that, \(\displaystyle 360^\circ=2\pi \Rightarrow 180^\circ=\pi\)

Thus, in order to convert from degrees to radians you need to multiply by . \(\displaystyle \frac{\pi}{180}\)

So in this particular case,

 \(\displaystyle 330*\frac{\pi}{180}=\frac{11\pi}{6}\).