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Complementary angles worksheets

Two complementary angles fit together into a right angle, so they add to 90 degrees. These free printable worksheets draw a pair with one marked x, cut from the mixed angle-pair page.

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Complementary angles
Complementary angles worksheet — Angles to 90 degrees, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The mixed angle-pair page rotates complementary, supplementary, and vertical relationships so a child has to decide which one the figure shows. This sheet drills just the complementary case, so the fact — the two make ninety — becomes automatic before the choosing begins.

Why this sheet works

Each figure shows two angles meeting at a square corner, with the corner mark that says they complete a right angle. The arithmetic is one subtraction from 90; the work is reading that the picture is a right angle in the first place, and writing the equation x + 65 = 90 before solving it.

How this one works

One question from this sheet, worked through a step at a time.

Angles in a right angle, one is 46°

46°+x=90°
90 − 46 =44°
46°+44°=90°
from the picture, not the numbers
lines crossing:x = the angle opposite
  1. 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.
  2. So the two must add to 90: x = 90 − 46 = 44°.
  3. 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.
  4. 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.

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