19. Find the value of x.

If we have two parallel lines cut by a transversal, then alternate interior angles are equal. Here we can see that the line intersected by angle x, and angles 135, and 45, can be extended to cut parallel lines with two $$135^{\circ}$$ angles. The angle adjacent to $$135^{\circ}$$ is $$180^{\circ}-135^{\circ}=45^{\circ}$$. Now we have an angle $$45^{\circ}$$ and an angle $$45^{\circ}$$ and $$x$$. The sum of angles in a triangle is 180. So, $$45+45+x = 180$$ then $$90+x=180$$, therefore $$x = 180-90=90^{\circ}$$. **Answer: 90°**