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Exterior in the Wild

Part of the Angles section of Coddy's Geometry journey. Lesson 53 of 59.

The exterior angle rule gives an equation when a label holds a letter: the exterior label equals the two remote labels added. It saves a step, because the angle inside at the corner never appears.

$Triangle KLM with exterior angle 125 degrees and remote angles x plus 15 and 60 degrees$

Here $\left(x+15\right)+60 = 125$ . Collect the numbers: $x+75 = 125$ , so $x = 50$ . The remote angle is 65°, and 65 + 60 = 125.

On the board, tap the exterior angle and its two remote angles and pick Exterior angle of a triangle. If the letter is on both sides, collect it on one side as usual.

Challenge

Triangle ABC has the side AC extended past C to D. Tap the angles you need, pick the rule that connects them, and solve the equation for x. Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

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 AnswerExterior in the WildRecap: 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