In a right-angled triangle ABC on the hypotenuse AB, points F and D are taken so that

In a right-angled triangle ABC on the hypotenuse AB, points F and D are taken so that AD = AC and BF = BC. Find the angle FCD if the angle ABC = 56 degrees.

The BFC triangle is isosceles, then the angle BFC = FCB = (180 – 56) / 2 = 62.

Determine the value of the angle BAC of the triangle ABC. Angle BAC = (180 – ACB – ABC) = (180 – 90 – 56) = 34.

The ACD triangle is isosceles, then the angle ACD = ADC = (180 – BAC) / 2 = (180 – 34) / 2 = 73.

In the CFD triangle, the angle FCD = (180 – FDS – DFC) = (180 – 73 – 62) = 45.

Answer: The value of the FCD angle is 45.