Answer:
AB = 4
[tex]m\angle E=30^\circ[/tex]
Step-by-step explanation:
Similar shapes
Two figures are similar if the ratios of the lengths of their corresponding sides are equal. The corresponding angles are also congruent.
Being ABCD and EFGH similar, the ratio of the lengths of AB and EF is equal to the ratio of the lengths of AD and EH, thus:
[tex]\displaystyle \frac{AB}{EF}=\frac{AD}{EH}[/tex]
Solving for AB:
[tex]\displaystyle AB=\frac{AD}{EH}\cdot EF[/tex]
Since AD=6, EH=1.5, and EF=1:
[tex]\displaystyle AB=\frac{6}{1.5}\cdot 1[/tex]
AB = 4
Since angle A is congruent to angle E:
[tex]m\angle E=m\angle A[/tex]
[tex]\mathbf{m\angle E=30^\circ}[/tex]
