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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.

 Mar 1, 2024
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Find the smallest angle, in degrees.

Hello blackpanther!

 

\(\alpha +\alpha +d +\alpha +2d=180^\circ\\ (\alpha +2d)-\alpha =56^\circ\\ d=28^\circ\\ 3\alpha +3\cdot 28^\circ =180^\circ\\ \alpha+28^\circ =60^\circ\\ \color{blue}\alpha =32^\circ\\ \beta =60^\circ\\ \gamma =88^\circ \)

\(\color{blue}\alpha ,the\ smallest\ angle\ is\ 32^\circ .\) 

 

laugh !

 Mar 2, 2024
edited by asinus  Mar 2, 2024

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