Question

problem 18: (first taught in lesson 30) if $ell_1parallelell_2$, 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 $180^{\circ}$. Let's consider the triangle formed.

Step2: Find the third - angle of the triangle related to the parallel lines

Since $\ell_1\parallel\ell_2$, the alternate interior angle to the non - right angle in the triangle (not $x$) formed by the transversal and the parallel lines is $32^{\circ}$.

Step3: Calculate $x$

We know that in the triangle, one angle is $90^{\circ}$ and another is $32^{\circ}$. Using the angle - sum property of a triangle ($a + b + c=180^{\circ}$, where $a = 90^{\circ}$, $b = 32^{\circ}$, and $c$ is the angle adjacent to $x$), we get $c=180-(90 + 32)=58^{\circ}$.
The angle $x$ and the $58^{\circ}$ angle are supplementary (linear pair). So $x=180 - 30=150^{\circ}$.

Answer:

$x = 150$