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The Exterior Angle

Part of the Angles section of Coddy's Geometry journey. Lesson 50 of 59.

Extend one side of a triangle past a corner, and a new angle opens outside the triangle, between the extension and the next side. That is an exterior angle. The two angles inside the triangle at the other corners are its remote interior angles, the ones far from it.

$Triangle KLM with LM extended past M: an exterior angle of 130 degrees at M, remote interior angles 55 and 75 degrees$

The exterior angle equals the sum of its two remote interior angles: here 55 + 75 = 130. Why: the exterior angle and the triangle's angle at the same corner sit on a straight line, so they add to 180. The three angles of the triangle add to 180 too. Take the shared corner angle away from both, and what is left on each side is equal.

The angle at the same corner, the neighbour of the exterior angle, is not remote. It is the one that makes 180 with it.

Challenge

Triangle ABC has the side AC extended past C to D, making the exterior angle ∠1. Tap its two remote interior angles, then press Check.

Try it yourself

$Find the right part on the figure$

Find the right part on 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 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 AngleUsing 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