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Using the Shortcut

Part of the Angles section of Coddy's Geometry journey. Lesson 51 of 59.

The exterior angle rule is a shortcut. The long way to an exterior angle takes two steps: find the angle inside at that corner, then its neighbour on the straight line. The shortcut adds the two remote angles in one.

$Triangle KLM with an exterior angle of 115 degrees at M and remote interior angles of 48 and 67 degrees$

With remote angles of 48° and 67°, the exterior angle is 48 + 67 = 115°. The long way agrees: the corner angle is 180 - 115 = 65°, and its neighbour on the line is 180 - 65 = 115°.

On the board the rule is Exterior angle of a triangle. It also works backwards: given the exterior angle and one remote angle, the other remote angle is the difference.

Challenge

Triangle ABC has the side AC extended past C to D. Find the exterior angle marked ? in one step, 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 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 ShortcutTwo 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