Draw the normal first

A protractor laid flat along the mirror is easier to read, and it gives you the wrong number: the complement of the angle the law is about.

A ray running $25^\circ$ above the glass has an angle of incidence of $65^\circ$, so the reflected ray also leaves at $65^\circ$ from the normal, which is $25^\circ$ above the glass on the other side. The final picture is the same either way in this case, which is why the habit survives, and the reported numbers are wrong.

The two ways of measuring agree only at $45^\circ$, which is exactly the case textbooks like to draw. So a worked example that comes out right at $45^\circ$ proves nothing about the method.

Every angle in this unit is measured the same way: reflection, refraction and the critical angle alike. One convention, applied everywhere.

Diffuse reflection is not the law being suspended. The law of reflection holds at every point of every surface. What changes on a rough surface is the direction of the normal, which tilts differently from point to point across the illuminated patch.

So zoom in on one microscopic facet: angle in equals angle out about that facet's own normal. Because the facet normals point every which way, parallel incoming rays leave in many directions.

That single difference explains a pair of everyday observations that otherwise look unrelated:

1. Smooth surface: one shared normal across the whole surface, so parallel rays stay parallel, and you see an image of whatever the light came from.
2. Rough surface: scattered normals, so the light fans out, and you see the surface itself from every seat in the room.

A sheet of paper and a mirror are made of the same kind of stuff doing the same thing at every point. The difference is the geometry at the scale of a wavelength.

Every point on an object sends light in all directions. Every one of those rays that reaches the mirror or lens is redirected to the same image point. The principal rays are chosen because their paths are easy to predict, not because they are the only light in the problem.

The consequence people get wrong: cover the top half of a converging lens with a card and you do not lose the top half of the image. You lose half the light that used to arrive, so the whole image survives at reduced brightness. Plenty of rays still get through the uncovered half, and they still cross at the same place.

The same reasoning applies to blocking a single principal ray. That ray was a construction aid; the light it stood for is still arriving by other paths.

Geometry fixes where the image is. The amount of light collected fixes how bright it is. Two separate questions, and mixing them is what produces half-images.

Four steps, in this order, and the order is the point.

1. Mark the point where the ray strikes the surface.
2. Draw the normal there, perpendicular to the surface. On a curved mirror that means perpendicular to the tangent at that point, which is along the radius.
3. Measure the angle of incidence from the normal to the incoming ray.
4. Lay the reflected ray on the other side of the normal, at the same angle.

Two useful checks. The incident ray, the reflected ray and the normal all lie in one plane. And the path is reversible: send a ray back along the reflected direction and it retraces the incident one exactly, which is why you can see someone in a mirror exactly when they can see you.