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Adding Adjacent Angles

Part of the Angles section of Coddy's Geometry journey. Lesson 5 of 59.

$Rays BA, BD and BC from B: angle ABD is 20 degrees, angle DBC is 50 degrees, and the whole angle ABC is unknown$

∠ABD is 20°. ∠DBC is 50°. They are adjacent: they are side by side and share the arm BD. Together they make ∠ABC. So ∠ABC is $20+50 = 70$ degrees. Adjacent angles add.

Three rays from B make three angles. So "the angle at B" is not clear. We name an angle with three points. The corner point goes in the middle: ∠ABD, ∠DBC and the big ∠ABC.

Challenge

Two rays cut ∠ABC into three parts: ?, 35° and 28°. ∠ABC is 85°. Find the part marked ?. Tap an angle and pick the reason, and its size appears. Then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

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 AnglesWrite 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 Mark Complementary Angles Perpendicular 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