What is the value of x? A. 9B. 8C. 10D. 4Explain please

Ok, here we go!

We know that two of the angles are congruent (the angles with two arcs are congruent and the angles with one arc are congruent). Since at least two angles are congruent, the triangles are similar. The corresponding sides of similar triangles are equal, so we can set up the equation:

8/12 = 6/x (you can read it "eight is to twelve as 6 is to x")
Multiply the means and extremes (12*6 and 8*x)
8x = 72
Now, divide 8 on both sides to isolate x:
x = 9

Now let's see if it checks out:
8/12 = 6/9 (divide both sides to check)
2/3 = 2/3

The correct answer is x = 9.

Hope this helps you =)