In the isosceles triangle CDE with the base CE, the height CF is drawn. Find the angle ECF if the angle is D = 54 (degrees).

1. By the condition of the problem, the SDE triangle is isosceles. Therefore, the angles at its base are equal. That is, the angle at vertex C is equal to the angle at vertex E.

2. We calculate the value of the angles at the vertices C and E, taking into account that the sum of the angles of the triangle is 180 °:

Angle C = angle E = (180 ° – 54 °) / 2 = 63 °.

3. Since according to the condition of the problem CF is the height drawn to the base of the DE of the triangle ECF, the angle CFE is 90 °.

4. We calculate the value of the angle ECF:

180 – 90 ° – 63 ° = 27 °.

Answer: The ECF is 27 °.