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Comparing Angles

When you look at animals opening their mouths, you can actually see angles being formed by their
jaws. Some mouths open wider than others, meaning they have larger angles.

Comparing angles by superimposition

 To compare two angles accurately, you can place one angle on top of the other, which is
called superimposition. For this to work, make sure the vertices of both angles overlap
exactly.

 After superimposing, it becomes easy to see which angle is smaller and which is larger. For
example, if you place ∠PQR on top of ∠ABC and the arms don’t match up, it will be clear
which angle is bigger.

Equal Angles

Now consider angles like ∠AOB and ∠XOY. How can you tell if they’re the same size?

 When comparing two angles, if the corners (vertices) match up perfectly and the arms (rays)
overlap exactly, like OA overlapping with OX and OB overlapping with OY, it means the angles
are equal in size.

 The reason these angles are considered equal is that if you think of each angle as being
formed by rotating a ray, the amount of rotation needed to move one ray to the other is the
same for both angles.