Answer:
x = 9/2 or 4.5
Explanation:
In order to solve this problem, you first need to identify whether or not the two triangles formed in the image are similar; you can tell that they are similar by the AAA property because they share a vertex, and the other two angles are congruent because of the Corresponding Angles Theorem. Now that you know the triangles are similar, you need to identify the corresponding sides:
x + 6 corresponds to x
21 corresponds to 9 (21 because 30 - 9 = 21)
You can find the scale factor by dividing 21 by 9:
21 ÷ 9 = 7/3
Now that you know the scale factor, you can write and solve an equation:
7/3x = x + 6 (given)
4/3x = 6 (subtract x from both sides)
x = 9/2 (multiply both sides by 3/4)