Question

(c) problem 18: (first taught in lesson 30) if $l_1\parallel l_2$, find $x$. after you enter your answer press go. $x = $

Explanation:

Step1: Use angle - sum property of triangle

The sum of interior angles of a triangle is $180^{\circ}$.

Step2: Find the third - angle of the triangle

Let's consider the triangle formed. One angle is $90^{\circ}$ (right - angle), and another angle related to the parallel lines. The angle adjacent to the $82^{\circ}$ angle and inside the triangle is $180 - 82=98^{\circ}$ (linear pair). The third angle of the triangle (let's call it $y$) and the $32^{\circ}$ angle are alternate interior angles (because $\ell_1\parallel\ell_2$), so $y = 32^{\circ}$.

Step3: Calculate $x$

We know that for the triangle with angles $90^{\circ}$, $98^{\circ}$ and $x^{\circ}$, $90 + 98+x=180$. Simplifying gives $188 + x=180$, so $x=180-(90 + 32+ 82)=18$.

Answer:

$18$