The 180 Rule
Part of the Angles section of Coddy's Geometry journey. Lesson 42 of 62.
The three interior angles of any triangle add to 180°. Here is why. Draw a line through the top corner, the apex, parallel to the base. The two base angles copy themselves up to the apex as alternate angles (the Z pairs, marked with matching arcs), and there the three angles sit side by side on a straight line: 180°.
Read it off the figure: at the apex, 60° and 50° are the copies and 70° sits between them, and 60 + 70 + 50 = 180 along the top line. The same three numbers are the triangle’s own corners, so they total 180° too. Thin, wide, lopsided or neat, every triangle spends exactly the same budget.
Challenge
EasyTwo angles of the triangle measure 65° and 70°; the third is x°.
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 Half9Triangle Angle Sum
The 180 RuleFinding the Third AngleTwo Unknown AnglesRight TrianglesRecap: The Budget