+1459 The interior angles of a polygon form an arithmetic sequence. The difference between the largest angle and smallest angle is $56^\circ$. If the polygon has $3$ sides, then find the smallest angle, in degrees.
+15000 Find the smallest angle, in degrees.
Hello blackpanther!
\(\alpha +\alpha +d +\alpha +2d=180^\circ\\ (\alpha +2d)-\alpha =56^\circ\\ d=28^\circ\\ 3\alpha +3\cdot 28^\circ =180^\circ\\ \alpha+28^\circ =60^\circ\\ \color{blue}\alpha =32^\circ\\ \beta =60^\circ\\ \gamma =88^\circ \)
\(\color{blue}\alpha ,the\ smallest\ angle\ is\ 32^\circ .\)
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