Question

True or false: If an angle is acute, then its complement must be greater than its supplement.

Answer 1

I'm pretty sure it's false, but I don't know how to explain why it's false.

Answer 2

False

Answer 3

Yes it is..

Answer 4

Ok, but how is it false?

Answer 5

If it is acute, then its compliment is \(90-x\)

And its Suppliment will be : \(180-x\)

Now, \(0 \le x \le 90\), let us say x = 45,

Then Compliment will be : \(90-45 = 45\)
And its suppliment will be : \(180-45 = 135\)..

Answer 6

Its because a supplementary angle has 180 degrees and complementary angle has to be 90 degrees so a complement angle cant be as big then the supplement angle. I think

Answer 7

Obviously, Supplement \((135)\) is greater than Complement (\(45\))..

Answer 8

Wow that helps a LOT!! Thanks!!!