Question

How do you find the degree measure of an angle?

Answer 1

Hint: To convert the radian measure to degree measure, we first multiply the radian measure by ${\left( {\dfrac{{180}}{\pi }} \right)^ \circ }$so as to get the angle in degree measure. Then to convert degree to minute, we multiply the degrees by $60'$ to get the result in minutes and to convert the minutes to seconds by multiplying $60''$ to the given number which is in minutes the resultant number will be in second.

Complete step-by-step answer:
There are two major units for measurements of angles. They are: the degree measure of an angle and radian measure of an angle. Radians and degrees are both units used for measuring angles. As you may know, a circle is composed of $2\pi $ radians, which is the equivalent of $360$ degree. Both of these values represent going once around a circle. Therefore, $1\pi $ radian represents going around a semi-circle or covering ${180^ \circ }$ of angle.
This makes $\dfrac{{{{180}^ \circ }}}{\pi }$ the perfect conversion tool for converting radians to degrees. To convert from radians to degrees, you simply have to multiply the radian value by $\dfrac{{{{180}^ \circ }}}{\pi }$.
Next, if the answer comes out in fraction or as a decimal, then one degree (°) is equal to $60$minutes (') and one minute equals sixty seconds. So, in turn, 1 degree is equal to $3600$ seconds. So, to convert decimal degrees to minutes, we multiply $60$ to the decimal degree number and next to convert decimal minute to seconds we multiply $60$ to the decimal minute.
For example: if we have to convert $6\pi $ radians into degree measures. We convert radian to degree by multiplying the radian measure by $\dfrac{{{{180}^ \circ }}}{\pi }$.
$ \Rightarrow 6\pi \times \dfrac{{{{180}^ \circ }}}{\pi }$
Cancelling $\pi $ in numerator and denominator, we get,
$ \Rightarrow 6 \times \dfrac{{{{180}^ \circ }}}{1}$
Doing the calculations, we get,
$ \Rightarrow {1080^ \circ }$
Next, we notice that we don’t have any decimal degrees. So, we don’t need to convert decimal degrees into minutes and subsequently decimal minutes into seconds. Hence, the degree measure for the given radian measure $6\pi $ is ${1080^ \circ }$.

Note: The way to distinguish between the two units of angle measurement is using the degree sign on the angle value whenever we are writing an angle in degree measure. Care should be taken while doing calculations. The factor $\dfrac{{{{180}^ \circ }}}{\pi }$ must be remembered for converting radian measure into degree measure.