Question

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

Answer 1

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=150º`Then, the angles of the octagon are: 126º,126º,126º,126º,126º,150º,150º,150º