Chapter 4, Problem 8CT

To determine

Value of x for the given condition.

Answer to Problem 8CT

The value of $x=3$

Explanation of Solution

Given:

In $\Delta ABC$

  $m\angle A=50,m\angle C=80,AC=7x+8\text{and}BC=38-3x$

From the given condition the figure obtained is,

  

Now,

  $\begin{array}{l}m\angle A+m\angle B+m\angle C=180\\ \Rightarrow 50+m\angle B+80=180\\ \Rightarrow m\angle B={50}^o\end{array}$

As, $m\angle A=m\angle B={50}^o$

It means $\Delta ABC$ is an isosceles triangle. So,

  $\begin{array}{l}AC=BC\\ \Rightarrow 7x+8=38-3x\\ \Rightarrow 7x+3x=38-8\\ \Rightarrow x=3\end{array}$

Therefore, the value of $x=3$