Answer:
8
Step-by-step explanation:
You want the measure of segment DE in the similar triangle figure shown.
Similar triangles
Alternate interior angles where a transversal meets parallel lines are congruent. This means ∠B≅∠C and ∠A≅∠D. The two triangles are similar by the AA postulate. This means corresponding sides are proportional:
[tex]\dfrac{AE}{AB}=\dfrac{DE}{DC}\\\\\\\dfrac{2x+10}{10}=\dfrac{x+3}{4}\qquad\text{substitute given values}\\\\\\2(2x+10)=5(x+3)\qquad\text{multiply by 20}\\\\4x+20=5x+15\qquad\text{eliminate parentheses}\\\\5=x\qquad\text{subtract $4x+15$}\\\\DE=x+3=5+3\\\\\boxed{DE=8}[/tex]
