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.
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.