How Many Angles in an Angle? [1)

I'm wondering if there are two angles in an
'angle.'

For example, the image below would typically be
identified as a right angle.

But couldn't you also say that it's a right angle
and a $270^o$ reflex angle? Are there two
angles?

http://tinyurl.com/4fs85kg



[2)

Or-- An equilateral triangle is defined (?) as a
triangle with three $60^o$ angles.

But couldn't you also say that an equilateral
triangle has three $300^o$ reflex angles? Six
angles?



[3)

Would the rays that form an angle be considered
straight angles?

If so: Since a ray consists of infinitely many
points.

And since any two points form a line segment.

And since a line segment can be considered a
straight angle.

Does it follow that an angle consists of infinitely
many angles?
You could also say it's a 90+360 = 450 degree angle, or any number $90+360n$ where n is a natural number. The point is, we say that it's 90 degrees clockwise or 270 mostly by convention, but yes, "an angle consists of infinitely many angles" is true.

Similarly for 2) you called it an "equiangular" triangle and so indeed by definition it must have three equal angles, however you measure them.

A "straight angle" would just be an angle of zero (or 360, or  720...) degrees.
By simply saying an angle, we mean the size of it is between 0 degree and 180 degrees. Its 360-degree counterpart should be marked with a prefix called reflex. Thus, there is no such thing as '2 angles in an angle'.