Two Roads, One Answer
Part of the Angles section of Coddy's Geometry journey. Lesson 55 of 62.
Every exterior angle problem can be walked two ways: the shortcut (pool the remotes) or the long road (budget to the interior corner, then supplement along the line). Trustworthy mathematics gives one answer twice.
Shortcut: z = 75 + 30, so z is 105. Long road: the interior corner takes 180 - 105, that is 75°, and the line then gives 180 - 75: 105 again. When two roads disagree, an error is hiding; when they agree, the answer has been checked for free.
Challenge
MediumThe remote interior angles measure 62° and 49°, the interior angle at C measures x°, and the exterior angle there measures 111°.
Find x. Two roads lead there; the canvas starts you on the budget road.
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