Question

find the value of x.

Explanation:

Step1: Note angle - sum property

The sum of angles around a point is $360^{\circ}$. Here, we have a right - angle ($90^{\circ}$) and three non - overlapping angles $(4x)^{\circ}$, $(6x)^{\circ}$, and $20^{\circ}$. So, $4x + 6x+90 + 20=360$.

Step2: Combine like terms

Combine the $x$ terms: $4x+6x = 10x$. The equation becomes $10x+90 + 20=360$, or $10x+110 = 360$.

Step3: Isolate the variable term

Subtract 110 from both sides of the equation: $10x=360 - 110$. So, $10x=250$.

Step4: Solve for x

Divide both sides by 10: $x=\frac{250}{10}$. Thus, $x = 25$.

Answer:

$25$