Exterior in the Wild
Part of the Angles section of Coddy's Geometry journey. Lesson 56 of 62.
In mixed figures the exterior angle is one clue among several: a remote corner may carry an expression while the exterior angle is the known. The theorem holds its shape: remote plus remote equals exterior, whichever part hides the x.
In the figure, (y + 10) + 45 = 130. Combine 10 + 45 into 55: y + 55 = 130, so y = 75. The labeled corner is 85°, and 85 + 45 pools to the stated 130: the theorem, read backwards, still reads true.
Challenge
MediumThe exterior angle measures 140°; the remote interior angles are (x + 25)° and 55°.
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