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Two Roads, One Answer

Part of the Angles section of Coddy's Geometry journey. Lesson 52 of 59.

A corner of a triangle with an extended side holds two angles: the one inside and the exterior one. Each can be found two ways, and the two ways must agree. That makes a good check on any chase.

$Triangle KLM with remote angles of 55 and 70 degrees and an extended side at M$

In the figure, the angles at K and L are 55° and 70°. Road one: the angle sum gives the inside angle at M, 180 - 55 - 70 = 55°, and the straight line gives the exterior angle, 180 - 55 = 125°. Road two: the exterior angle rule gives 55 + 70 = 125° at once, and the straight line gives the inside angle back.

Pick either road on the board. Once one angle at the corner is known, the other is its neighbour on the straight line.

Challenge

Triangle ABC has the side AC extended past C to D. Find both angles marked ? at C, the one inside and the one outside, 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 Angle Using the ShortcutTwo Roads, One AnswerExterior 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