Complementary angles, step by step

Two complementary angles fit together into a right angle, so they add to 90 degrees.

The question

degrees

Angles in a right angle, one is 33°

33°+x=90°

90 − 33 =57°

33°+57°=90°

from the picture, not the numbers

lines crossing:x = the angle opposite

The two angles fill a RIGHT ANGLE — look for the little square in the corner, because that is the mark that tells you it is 90 and not 180.
So the two must add to 90: x = 90 − 33 = 57°.
If it had been the other kind you would have taken it from 180 instead and been 90° out — which is why the picture is read first.
One more shape to know: where two straight lines CROSS, the two angles facing each other are equal — nothing is taken away at all. Subtracting there would be wrong.

How it works.

01
The two angles fill a RIGHT ANGLE — look for the little square in the corner, because that is the mark that tells you it is 90 and not 180.
02
So the two must add to 90: x = 90 − 33 = 57°.
03
If it had been the other kind you would have taken it from 180 instead and been 90° out — which is why the picture is read first.
04
One more shape to know: where two straight lines CROSS, the two angles facing each other are equal — nothing is taken away at all. Subtracting there would be wrong.