Both Angles Labeled
Part of the Angles section of Coddy's Geometry journey. Lesson 37 of 62.
Co-interior angles between parallel lines add to 180°, even when both measures are given by expressions. Put parentheses around each expression, add them, and set the sum equal to 180.
In the figure, (2y + 40) + (y + 20) = 180. Collect the y terms and the numbers: 3y + 60 = 180, so 3y = 120 and y = 40. The two angles come out 120° and 60°, and their sum checks: the algebra grew, the geometry did not.
Challenge
MediumThe marked angles are co-interior: (3x + 15)° 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 Turn8Transversal Problems
Both Angles LabeledVerticals Meet ParallelsFrom Figure to EquationAlternate with AlgebraRecap: Through the Strip3Right 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