In an isosceles triangle CDE with base CE, the height CF is drawn and find the angle ECF. If the angle is D = 54.

The angle D at the apex of an isosceles triangle is known by condition, we find the angle DCE at the base:
∠ DCE = (180 ° – ∠ CDE) / 2 = (180 ° – 54 °) / 2 = 126 ° / 2 = 63 °.
Consider a right-angled triangle DFC (CF is the height by condition) and find the second acute angle DCF in it:
∠ DCF = 90 ° – ∠ CDE = 90 ° – 54 ° = 36 °.
Find the ECF as part of the DCE:
∠ ECF = ∠ DCE – ∠DCF = 63 ° – 36 ° = 27 °.
Answer: The degree measure of the ECF angle is 27 °.