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Is there a name for and angle larger than 0 and smaller than $\pi$ or 180 degrees? So it covers acute, right and obtuse, it's kind of opposite of reflex angle. In my language there is a name for such an angle, so I'd be surprised if there isn't one in English. The term would then apply to every angle of a polygon iff that polygon is convex.

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    $\begingroup$ Not sure how standard this is, but one source calls it a "convex angle." proofwiki.org/wiki/Definition:Convex_Angle $\endgroup$ – Thomas Andrews Jun 30 '16 at 19:23
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    $\begingroup$ It may not be standard (I've never heard it, and I've been messing with geometry for a half-century), but if someone told me they had a "convex angle", I'd know that this was what they meant, so it seems like a pretty good term. :) $\endgroup$ – John Hughes Jun 30 '16 at 19:25
  • $\begingroup$ Good question. But note, that some functions are defined for $\alpha \in [-\pi/2,\pi/2]$ $\endgroup$ – Yuriy S Jun 30 '16 at 19:26
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Looks like some sources call this a "convex angle," because the interior of the angle is a convex set.

For example, PlanetMath and ProofWiki use this definition.

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My GSCE maths textbook describes such an angle as an ordinary angle. Acute and obtuse angles are both ordinary angles, reflex angles are not ordinary angles. An ordinary angle is any angle from 0 to 180 degrees.

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