# 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?

• Say what you like — as long as it is consistent and, preferably, leads to interesting conclusions. But you will confuse people if you drift too far from the conventional. (I cannot make much sense of / see much use for [3).) – PJTraill Nov 10 '16 at 0:11

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.