Exercise 2: Prove that the triangle ULM is isosceles.

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

In the triangle LME, the sum of the angles equals 180°.

Thus angle LUM = angle ULM = 65°.
In the triangle ULM, angle LUM = 180 - (50 + 65) = 65°.
As the points U, M and E are aligned, the angle UME measures 180°.
Thus angle LME = 180 - ( 25 + 40) = 115°
Thus angle UML = 180 - 115 = 65°
Thus the triangle ULM has two congruent angles.
Thus the triangle ULM is isosceles at U.