I just need to know if I answered this correctly.

mLy=37 find the complementary angle Ly

That would be 90-37= correct?

Correct!

a complementary angle finds the other angle needed to "complete" it into a 90 degree angle, so x (37) and
90 - x (90 - 37) is the way

so Ly=53

Thank you for the response. I appreciate it.

Yes, that is correct! To find the complementary angle, you need to subtract the given angle from 90 degrees. In this case, mLy is given as 37. So, subtracting 37 from 90 gives you the complementary angle, which is 53 degrees. Well done!