If the measure of an angle is 23o17’18’’, what is the measure of its supplement?
The supplement, s, of an angle is such that the sum of the angle and s makes 180 degrees.
So s=180-angle = 180-23°17'18".
There are 60' in one degree, and there are 60" in 1'.
For example, the supplement of 24°32'24" is 155°27'36".
To find the measure of the supplement of an angle, you need to subtract the measure of the angle from 180 degrees.
In this case, the given angle is 23 degrees, 17 minutes, and 18 seconds (23° 17' 18'').
There are 60 minutes in a degree, so first we convert the 17 minutes to degrees by dividing it by 60:
17 minutes / 60 = 0.2833 degrees
Similarly, there are 60 seconds in a minute, so we convert the 18 seconds to degrees by dividing it by 3600:
18 seconds / 3600 = 0.005 degrees
Now we add up the degrees, minutes, and seconds to get the total measure of the angle in degrees:
23 degrees + 0.2833 degrees + 0.005 degrees = 23.2883 degrees
To find the measure of the supplement, we subtract the measure of the angle from 180 degrees:
180 degrees - 23.2883 degrees = 156.7117 degrees
Therefore, the measure of the supplement of the given angle is 156.7117 degrees.