Question

find the value of x.
(11x - 12)°
36°
x =

Explanation:

Step1: Note angle - sum property

The sum of angles around a point is $360^{\circ}$. Here, we have a right - angle ($90^{\circ}$), an angle of $36^{\circ}$, and an angle of $(11x - 12)^{\circ}$. The remaining angle is also a right - angle ($90^{\circ}$) since the lines are perpendicular. So, $90+36+(11x - 12)+90 = 360$.

Step2: Simplify the left - hand side

Combine like terms: $(90 + 36-12 + 90)+11x=360$.
$204 + 11x=360$.

Step3: Solve for x

Subtract 204 from both sides: $11x=360 - 204$.
$11x = 156$.
Divide both sides by 11: $x=\frac{156}{11}\approx14.18$. But if we assume the non - shown angles are right - angles and we consider the non - overlapping part of the given angles, we have $(11x - 12)+36=90$ (since the two non - right angles make up a right - angle).

Step4: Solve the new equation for x

First, simplify the left - hand side of $(11x - 12)+36 = 90$ to get $11x+24 = 90$.
Subtract 24 from both sides: $11x=90 - 24$.
$11x = 66$.
Divide both sides by 11: $x = 6$.

Answer:

$x = 6$