Question

In the figure above, point $B$ lies on side $\overline{AC}$. If $55<x<60$, what is one possible value of $y$ ?

• A. $115<y<125$
• B. $120<y<125$
• C. $120\le y\le 125$
• D. None of these

Answer 1

The correct option is B $120<y<125$

Given, point ${}^{\prime }{B}^{\prime }$ lies on side $\overrightarrow{AC}$ and $55$ $<$ $x$ $<$ $60$.

We know that $\angle$$ABC$ $=$ $180$

$\Rightarrow x$ $+$ $y$ $=$ $180$

$\Rightarrow x$ $=$ $180$ $-$ $y$

As $55$ $<$ $x$ $<$ $60$

$\Rightarrow 55$ $<$ $180$ $-$ $y$ $<$ $60$

$\Rightarrow 55$ $-$ $180$ $<$ $-$ $y$ $<$ $60$ $-$ $180$

$\Rightarrow -125$ $<$ $-y$ $<$ $-120$

$\Rightarrow 120$ $<$ $y$ $<$ $125$