Respuesta :

First the two angles are equal to one another so take note of that.

Now setup the equation which will be

x+90=4x

Now get rid of alike terms

So subtract x from both sides

90=3x

Now divide 90 by 3

x=30

Answer:  The correct option is

(C) x = 30.

Step-by-step explanation:  We are given to find the value of x from the figure shown.

From the figure, we note that the angles with measures (x+90)° and 4x° are vertically opposite angles.

Since the measures of two vertically opposite angles are equal, so we must have

[tex](x+90)^\circ=4x^\circ\\\\\Rightarrow x+90=4x\\\\\Rightarrow 4x-x=90\\\\\Rightarrow 3x=90\\\\\Rightarrow x=\dfrac{90}{3}\\\\\Rightarrow x=30.[/tex]

Thus, the required value of x is 30.

Option (C) is CORRECT.