Two Roads, One Answer
Part of the Angles section of Coddy's Geometry journey. Lesson 55 of 62.
You can find an exterior angle by adding the two remote interior angles. Alternatively, subtract their sum from 180° to find the adjacent interior angle, then subtract that angle from 180°. Both calculations give the same exterior angle.
The exterior-angle theorem gives z = 75 + 30 = 105. Alternatively, the adjacent interior angle is 180 - 75 - 30 = 75 degrees, so z = 180 - 75 = 105. Both methods give 105°.
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. The canvas starts with the equation for the triangle's interior angle sum.
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