Final answer:
The equation needed to find the value of x in the triangle is 12x = 180 because the sum of angles in a triangle is 180 degrees, and after subtracting the known right angle of 90 degrees and another given angle of 20 degrees, the remaining angle is 70 degrees, which is equal to 12x.
Thus, the correct option is B.
Step-by-step explanation:
To determine the value of x in the given triangle, one must understand the properties of the triangle and relate that to the known angles and the sum of angles in a triangle. The sum of the angles in any triangle is 180 degrees.
If the triangle in question is a right triangle with one angle of 20 degrees, the other angle can be calculated by subtracting the known angles from 180 degrees:
180 degrees (sum of angles in a triangle) - 90 degrees (right angle) - 20 degrees (given angle) = 70 degrees for the other angle.
Therefore, if the expression for the other angle is 12x, then 12x = 70, which simplifies to 12x = 180 - 90 - 20 or 12x = 70.
Thus, the equation needed to find the value of x is B. 12x = 180.