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Complementary Angles

Part of the Angles section of Coddy's Geometry journey. Lesson 9 of 59.

Two angles whose sizes add up to 90° are complementary, and each is the complement of the other. The complement of 30° is 60°, because together they make a right angle.

$A right angle split by a ray into 30 and 60 degrees$

The usual place to meet them is a right angle cut in two by a ray. The square says the whole corner is 90°, so its two parts must share those 90°: 30° and 60° here. Knowing one part, you find the other by taking it from 90.

The rule on the board is Parts of a right angle: it applies to the pieces of a corner that carries the square. Pick it for the piece you want.

Challenge

The ray BD splits the marked right angle ABC. Find ∠DBC, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

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

All lessons in Angles

1Meet the Angle

Your First Angle Angles on a Line Degrees and the Full Turn Across the Crossing

4Vertical Angles

Two Lines Cross Vertical Angles Are Equal Solving with Verticals All Four Angles Recap: At the Crossing

7Parallels and Transversals

Parallel Lines Corresponding Angles Alternate Angles Co-interior Angles Which Rule Is It Recap: The Three Pairs

10Isosceles and Equilateral

Base Angles Are Equal Finding the Apex Which Angles Match Equilateral Angles Isosceles at Work Recap: Twin Corners

2Naming and Equations

Adding Adjacent Angles 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

8Angle Chases

Verticals Meet Parallels Is There Enough?From Figure to Equation Both Angles Labeled 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

The Square MarkComplementary AnglesPerpendicular Lines Finding the Complement 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