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Math Help - 9th Grade Easy Triangle Question For Most

  1. #1
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    Cool 9th Grade Easy Triangle Question For Most

    The three angles of a triangle have measures 12x degrees, 3x degrees, and 7y degrees, where 7y is greater than 60. If x and y are integers, what is the value of X?
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    Quote Originally Posted by 4woods View Post
    The three angles of a triangle have measures 12x degrees, 3x degrees, and 7y degrees, where 7y is greater than 60. If x and y are integers, what is the value of X?
    Solve 15x + 7y = 180, where 7y > 60 and x and y are whole numbers, by trial and errror.

    eg. y = 9 => 7y = 63 satisfies the first condition. But 15x = 180 - 63 = 117 does not have a solution for x that's a whole number. So try again ....
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    Hello, 4woods!

    The three angles of a triangle have measures 12x degrees, 3x degrees,
    and 7y degrees, where {\color{red}\rlap{///////}}7y > 60 .
    Unnecessary and confusing . . .

    If x and y are integers, what is the value of x ?

    The three angles of a triangle always total 180.

    Hence: . 12x + 3x + 7y \:=\:180 \quad\Rightarrow\quad x \:=\:\frac{180-7y}{15} \:=\:12 - \frac{7y}{15}

    Since x is an integer, y must be a multiple of 15.

    \text{Since }7y < 180\text{, then }\,y < 26.\;\;\text{ Hence: }\:y = 15.

    Therefore: . x \;=\;12 - \frac{7(15)}{15} \quad\Rightarrow\quad \boxed{x \:=\:5}

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