Answer:
BE = 24
Explanation:
These triangles are similar because of AA (Angle, Angle)
The given gives us a pair of parallel sides, allowing us to see that angles C and B are congruent due to being alternate interior angles.
Furthermore, we see that <AEB = <CEB due to vertical <'s being =
Next, we must set up a proportion;
If we create a proportion between the triangles, we must divide corresponding sides;
52/26 = 5x -7 / 2x+2 because we divided both triangles by using the same corresponding sides divided by the same corresponding side.
Simplify 52/26 to 2 and we get that 2 = 5x-7 / 2x+2
Multiply both sides by 2x+2 to get 4x+4 = 5x-7
Subtract 4x from both sides and add 7 from the right side to isolate x and get x=11
Finally, substitute the value of 11 for x into BE 2(11) + 2 and get 22 + 2 =24