Solving with Verticals
Part of the Angles section of Coddy's Geometry journey. Lesson 19 of 62.
When both vertical angles carry expressions, the equal sign does the work: set one label equal to the other and solve. The unknown now lives on both sides, which changes nothing about the method: collect the x’s on one side, the numbers on the other.
In the figure, 3y - 10 = 2y + 20. Take 2y from both sides: three y’s take away two y’s leave one y, so y - 10 = 20. Add 10 to both sides: y = 30. Both labels then read 80°, as an opposite pair should. That final check, feeding the answer back into both labels, catches sign slips before they cost anything.
Challenge
MediumThe opposite angles at the crossing are labeled (3x - 20)° and (2x + 10)°.
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 Turn3Right 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