Using the Shortcut
Part of the Angles section of Coddy's Geometry journey. Lesson 54 of 62.
The exterior angle theorem shines when the outside angle carries the expression: set it equal to the sum of the remotes and solve, no inside corner needed.
In the figure, y + 30 = 60 + 50. The right side gathers into 110, so y = 80. The exterior label then reads 110°, exactly what the two remotes pool. Working through the interior corner instead costs two extra moves and lands in the same place.
Challenge
MediumThe exterior angle measures (2x + 15)°; the remote interior angles are 45° and 70°.
Find x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Angles
1Meet the Angle
Your First AngleNaming AnglesAdding Adjacent AnglesDegrees and the Full TurnAcute, Right, ObtuseRecap: Adjacent Angles4Vertical Angles
Linear PairsVertical Angles Are EqualSolving with VerticalsAll Four AnglesRecap: At the Crossing2Straight Lines and Supplements
Angles on a LineSupplementary AnglesThree Angles on a LineWrite the EquationRecap: Along the Line5Around a Point
Angles Around a PointThe Missing AngleEqual SlicesFour Angles, One PointRecap: The Full Turn8Transversal Problems
Both Angles LabeledVerticals Meet ParallelsFrom Figure to EquationAlternate with AlgebraRecap: Through the Strip11The Exterior Angle
The Exterior AngleUsing the ShortcutTwo Roads, One AnswerExterior in the WildRecap: Outside View3Right Angles and Complements
Complementary AnglesFinding the ComplementPerpendicular LinesEqual Parts of a CornerRecap: The Right Corner6The Angle Bisector
The Angle BisectorBisected ExpressionsBisecting a Straight AngleRecap: Split in Half