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[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The given figure is of a regular octagon, and we know that each interior Angle of a regular octagon is equal to :

  • [tex] \dfrac{180 \times (8 - 2)}{8} [/tex]

  • [tex] \dfrac{180 \times 6}{8} [/tex]

  • [tex] \dfrac{1080}{8} [/tex]

  • [tex]135[/tex]

so, interior angle of octagon = 135°

now, according to above question,

Exterior Angle (6x - 21)° is forming linear pair with interior Angle of the octagon, so their sum will be equal to 180° .

  • [tex]6x - 21 + 135 = 180[/tex]

  • [tex]6x + 114 = 180[/tex]

  • [tex]6x = 180 - 114[/tex]

  • [tex]6x = 66[/tex]

  • [tex]x = 11 \degree[/tex]

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