Answer :
The complementary angles for 36°47'50" is 53°12'10”, while the supplementary angle is 143°12'10”. These are calculated by subtracting the given angle from 90 degrees for the complementary angle or from 180 degrees for the supplementary angle, converting from degrees to seconds and back for easier calculations.
In Mathematics, complementary angles are two angles that add up to 90 degrees, or a right angle. With the given angle of 36°47'50", it means we want to find an angle that would add up with it to make exactly a right angle (90 degrees). On the other hand, supplementary angles are angles that when summed, are equal to 180 degrees or a straight angle. So for this angle, we are exploring the angle that when added to it, equals exactly a straight line or 180 degrees.
To find the complementary angle you subtract the given angle from 90 degrees:
Convert everything to seconds for easier calculations: 36°47'50" equals 132470 seconds
Next, convert 90 degrees to seconds: 90° equals 324000 seconds
Subtract the given angle in seconds from 90 degrees in seconds: 324000 - 132470 = 191530 seconds
Convert this back to degrees, minutes, and seconds we get: 53°12'10”
This is your complementary angle. Similarly, the supplementary angle is found by subtracting the given angle from 180 degrees:
First, convert 180 degrees to seconds: 180° equals 648000 seconds
Subtract your given angle in seconds from 180 degrees in seconds: 648000 - 132470 = 515530 seconds
Convert this back to degrees, minutes, and seconds we get: 143°12'10”
This is your supplementary angle.
Learn more about angles here:
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