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?
Hello, 4woods!
The three angles of a triangle have measures $\displaystyle 12x$ degrees, $\displaystyle 3x$ degrees,
and $\displaystyle 7y$ degrees, where $\displaystyle {\color{red}\rlap{///////}}7y > 60$ . Unnecessary and confusing . . .
If $\displaystyle x$ and $\displaystyle y$ are integers, what is the value of $\displaystyle x$ ?
The three angles of a triangle always total 180°.
Hence: .$\displaystyle 12x + 3x + 7y \:=\:180 \quad\Rightarrow\quad x \:=\:\frac{180-7y}{15} \:=\:12 - \frac{7y}{15}$
Since $\displaystyle x$ is an integer, $\displaystyle y$ must be a multiple of 15.
$\displaystyle \text{Since }7y < 180\text{, then }\,y < 26.\;\;\text{ Hence: }\:y = 15$.
Therefore: .$\displaystyle x \;=\;12 - \frac{7(15)}{15} \quad\Rightarrow\quad \boxed{x \:=\:5}$