Answer:
The measure of angle E is 55°
Step-by-step explanation:
In an isosceles triangle, the vertex angle is the angle including between the two equal sides, the base angles are the other angles of the triangle, the base angles are equal in measures
In triangle DEF
∵ DE is congruent to FD
∴ The length of DE = the length of FD
∵ ∠D is the angle including sides DE and FD
∴ ∠D is the vertex angle
∴ ∠F and ∠E are the base angles
∵ The base angles of the isosceles triangle are equal in measures
∴ m∠F = m∠E
∵ m∠F = 55°
∴ m∠E = 55°
∴ The measure of angle E is 55°
