Question

In the figure above, point B lies on $\overline{AC}$. Find a possible value of $X$, if $X$ and $Y$ are integers.

• A. ${30}^o$
• B. ${35}^o$
• C. ${40}^o$
• D. ${50}^o$
• E. 55

Answer 1

The correct option is A ${30}^o$

From the figure, we can observe that
$X^0+Y^0+Y^0+Y^0={180}^0$

$X^0+3Y^0={180}^0$

$X^0=180-3Y^0$

$X^0=3({60}^0-Y^0)$

Since both $X$ and $Y$ are integers, hence '$X$' is a multiple of $3$.

Thus ${30}^0$ is a possible answer.