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Math Help - Find Measure of Angle C

  1. #1
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    Find Measure of Angle C

    In triangle ABC, the measure of angle B is twice the measure of angle A. If the measure of angle A is subtracted from the measure of angle C, the difference is 20. Find the measure of angle C.

    My answer is 120 degrees.

    The book's answer is 60 degrees.
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  2. #2
    Senior Member Twig's Avatar
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     A + B + C = 180 \; \mbox{ and } C-A=20 \; \mbox{ and } -2A+B=0

    \left[\begin{matrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 2 & -1 & 0 \end{matrix}\right] \left[\begin{matrix} A \\ B \\ B \end{matrix}\right]

    Solving this linear system of equations yields  C = 60 .
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  3. #3
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    twig...

    Quote Originally Posted by Twig View Post
     A + B + C = 180 \; \mbox{ and } C-A=20 \; \mbox{ and } -2A+B=0

    \left[\begin{matrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 2 & -1 & 0 \end{matrix}\right] \left[\begin{matrix} A \\ B \\ B \end{matrix}\right]

    Solving this linear system of equations yields  C = 60 .
    I notice that you decided to use matrix algebra to show the answer. Can you set this up for me using a system of linear equations in 3 unknowns?
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  4. #4
    Senior Member Twig's Avatar
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    hi

    Uhm, is this what you mean?

     \{A+B+C=180\}
    \{C-A=20\}
    \{-2A+B=0\}

    PS: If anyone could show the code for making a "large bracket" around all of the equations plz =)
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  5. #5
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    ok...

    Quote Originally Posted by Twig View Post
    hi

    Uhm, is this what you mean?

     \{A+B+C=180\}
    \{C-A=20\}
    \{-2A+B=0\}

    PS: If anyone could show the code for making a "large bracket" around all of the equations plz =)
    I will use this system of linear equations in 3 variables to find the answer.
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