Complementary Angles

Part of the Angles section of Coddy's Geometry journey. Lesson 12 of 62.

Two angles whose measures add to 90° are complementary: together they fill a right angle exactly. Each is the complement of the other.

$A right angle split into 30 and 60 degrees$

In the figure the corner carries the square, so the whole is exactly 90°, and the parts obey 30 + 60 = 90: 30° and 60° are complements. Given one, the other is forced: the complement of 30° is 90 - 30, which is 60°.

Challenge

Easy

The corner in the figure is a right angle, split into two parts: 55° and x°.

$A right angle split into 55 degrees and x degrees$

Find x.

Try it yourself

x + 55 = 90

Solve for x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Angles

2Straight Lines and Supplements

Angles on a Line Supplementary Angles Three Angles on a Line Write the Equation Recap: Along the Line

5Around a Point

Angles Around a Point The Missing Angle Equal Slices Four Angles, One Point Recap: The Full Turn

8Transversal Problems

Both Angles Labeled Verticals Meet Parallels From Figure to Equation Alternate with Algebra Recap: Through the Strip

11The Exterior Angle

The Exterior Angle Using the Shortcut Two Roads, One Answer Exterior in the Wild Recap: Outside View

3Right Angles and Complements

Complementary AnglesFinding the Complement Perpendicular Lines Equal Parts of a Corner Recap: The Right Corner

6The Angle Bisector

The Angle Bisector Bisected Expressions Bisecting a Straight Angle Recap: Split in Half

9Triangle Angle Sum

The 180 Rule Finding the Third Angle Two Unknown Angles Right Triangles Recap: The Budget

12Final Challenges

Final: The Angle Chase Final: Triangle Meets Line Final: The Full Round Final: Isosceles Chase Final: Master of Angles