# SOLUTION: Given: Triangle ABC Prove: m<4= m<1 + m<2 Picture: A triangle with line, CD, connected to it. A is m<1, B is m<2, C is m<3, and m<4 are vertical angles to m<3

Algebra ->  Algebra  -> Geometry-proofs -> SOLUTION: Given: Triangle ABC Prove: m<4= m<1 + m<2 Picture: A triangle with line, CD, connected to it. A is m<1, B is m<2, C is m<3, and m<4 are vertical angles to m<3      Log On

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 Geometry: Proofs in Geometry Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Geometry proofs Question 257494: Given: Triangle ABC Prove: m<4= m<1 + m<2 Picture: A triangle with line, CD, connected to it. A is m<1, B is m<2, C is m<3, and m<4 are vertical angles to m<3Answer by drk(1908)   (Show Source): You can put this solution on YOUR website!This is also called the exterior triangle theorem. With angle 4 vertical to angle 3, you cannot prove angle 4 = angle 1 + angle 2. For this to work, angle 4 must be supplementary to angle 3. Here is the proof for that. STATEMENT 1: triangle ABC REASON 1: given STATEMENT 2: angle 1 + angle 2 + angle 3 = 180 degrees REASON 2: definition of sum of angles of triangle STATEMENT 3: angle 3 + angle 4 = 180 REASON 3: definition of supplementary angles STATEMENT 4: angle 1 + angle 2 + angle 3 = angle 3 + angle 4 REASON 4: substitution [2,3] STATEMENT 5: angle 1 + angle 2 = angle 4 REASON 5: subtraction property of equality