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[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?

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  • $\begingroup$ 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).) $\endgroup$ – PJTraill Nov 10 '16 at 0:11
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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.

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  • $\begingroup$ You mean a straight angle would be 180, 540... $\endgroup$ – JNF Feb 6 '13 at 18:08
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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.

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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'.

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