The two angles shown are vertical angles. They form when you cross two lines. They are opposite one another. Note: They don't have to be vertically up and down in relation to each other. It's possible to have them horizontally side by side like this.
So because they are vertical angles, they are congruent. This means they are equal in measure
x+90 = 4x
x+90-x = 4x-x
90 = 3x
3x = 90
3x/3 = 90/3
x = 30
Therefore the answer is choice C) The value of x is x = 30
We can check it by plugging this into the original equation above
x+90 = 4x
30+90 = 4*30
120 = 120
our answer checks out