Question

find the value of x.

Explanation:

Step1: Identify angle - sum relationship

The sum of angles around point $W$ is $360^{\circ}$, and the right - angle is $90^{\circ}$. So, $4x + 6x+90 + 20=180$ (considering the non - reflex angles in the diagram).

Step2: Combine like terms

Combine the $x$ terms: $4x+6x = 10x$. The equation becomes $10x+90 + 20=180$.

Step3: Simplify the left - hand side

$10x+110 = 180$.

Step4: Isolate the variable term

Subtract 110 from both sides: $10x=180 - 110$.
$10x = 70$.

Step5: Solve for $x$

Divide both sides by 10: $x=\frac{70}{10}=7$.

Answer:

$7$