Exercise 1: Work out the orange angle.

This is the beginning of the proof.
Put the next steps in order.

As the triangle CTL is equilateral, each of its angles measures 60°.

Thus angle TCF = 60 + 45 = 105°.
Thus angle TCL measures 60°.
Thus the angles LCF and CFL are congruent.
As the triangle CLF is right angled at L, the angles LCF and CFL are complementary.
But the triangle CLF is also isosceles at L.
Thus angle LCF + angle CFL = 90°.
Thus angle LCF = angle CFL = 45°.
Thus angle TCF measures 105°.