Chapter 5.2, Problem 26PSC

To determine

To Find: The value of $x$ for which $m\parallel n$ , with explanation.

Answer to Problem 26PSC

  $x\approx 6,0$

Explanation of Solution

Given:

  

Concept Used:

When parallel line in intersected by a transversal corresponding angles are equal.

Calculation:

Here, $m\parallel n$ , corresponding angles on the same side of transversal are equal.

  $\begin{array}{l}{\left(x^2+10\right)}^{\circ }={\left(3x+17\right)}^{\circ }\\ \Rightarrow x^2-3x+10-17=0\\ \Rightarrow x^2-3x-7=0\\ \Rightarrow x=\frac{-\left(-3\right)\pm \sqrt{3^2-4\left(1\right)\left(-7\right)}}{2\left(1\right)}\\ =\frac{3\pm \sqrt{37}}{2}\\ =\frac{3+\sqrt{37}}{2},\frac{3-\sqrt{37}}{2}\\ =6.04,-0.04\\ \therefore x\approx 6,0\end{array}$