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In an octagon, five of the angles are equal and each of the other three angles is 24° greater than each of the five other ones. Determine the angles of the octagon anto

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Given:

5 angles are equal: x

Each of the other angles is 24 greater than the other 5 angles: x+24

An octagon has 8 angles; the sum of the interior angles of an octaogn is 1080º


5x+3(x+24)=1080º

Use the equation above to solve x:


\begin{gathered} 5x+3x+72=1080 \\ 8x+72=1080 \\ 8x=1080-72 \\ 8x=1008 \\ x=(1008)/(8) \\ \\ x=126 \end{gathered}

The 5 angles that are equal measure 126º

The other 3 angles measure:


x+24=126+24=150ºThen, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150º
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