Answer:
x = 12
Step-by-step explanation:
From the diagram, we are given one angle on a straight line, which is 130 degrees. We know that a straight line is 180 degrees, so we can find the angle directly opposite the given one:
180 - 130 = 50
We also know that the interior angles of a triangle must add up to 180. In addition, we know that vertical angles are always congruent.
Given this information, we can now write an equation, in terms of x, for all the angles inside this triangle:
180 = (3x - 6) + (8x + 4) + 50
We now do basic algebra to solve for x:
180 = 11x + 48
132 = 11x
12 = x
And therefore x = 12.
