Question 228666
Let x = the angle
90-x= the complement
180-x= the supplement


"the difference between the measures of its supplement and 3 times its complement is 10"


(180-x)-3(90-x)=10

180-x-270+ 3x=10
-90 +2x = 10


Add 90 to each side:
2x= 100
x=50 degrees = The angle

Complement = 90-50=40 degrees
Supplement = 180-50=130 degrees

Check:  3 times the complement = 3(40)=120 degrees

The difference between the supplement and 3 times the complement is 10 degrees, so it checks!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida