The Exterior Angle
Part of the Angles section of Coddy's Geometry journey. Lesson 53 of 62.
Extend one side of a triangle past a corner and a new angle opens on the line outside: the exterior angle. It equals the sum of the two remote interior angles, the ones far from it. Why: the exterior angle supplements the interior at its corner, and so do the other two combined.
In the figure the exterior angle reads 110°, and one remote corner reads 40°: y + 40 = 110, so y = 70. One equation replaces a two-step trip through the inside corner.
Challenge
EasyThe side through C is extended. The exterior angle measures 120°, and the remote interior angles are x° 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