How Many Angles in an Angle?

Question

[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-degree reflex angle? There are two angles?

http://tinyurl.com/4fs85kg

---

[2)

Or-- An equiangular triangle is defined (?) as a triangle with three 60-degree angles.

But couldn't you also say that an equiangular triangle has three 300-degree 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?

Answer 1

It depends on how you measure angles. If you measure counterclockwise, you will get the usual angles. If you measure clockwise, you will get the other ones you mention.

Answer 2

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.