Question

Can somebody help me with this question

Answer 1

`\text{a) }1,080^(\circ), \\\text{b) }360^(\circ), \\\text{c) }135^(\circ), \\\text{d) }45^(\circ)`

Explanation:

a) The sum of the interior angles of a polygon with
`n` sides is equal to
`(n-2)180`. Since an octagon has 8 sides, substitute in
`n=8`:

`(6-2)180=\boxed{1,080^(\circ)}`

b) The sum of the exterior angles for any polygon is equal to
`360^(\circ)`.

c) By definition, all regular shapes have equal angles and sides. Since we've found the total sum of the interior angles of an octagon in part a, each interior angle of a regular octagon must be
`(1080)/(8)=\boxed{135^(\circ)}`

d) Similar to part c, all regular shapes must have equal angles and sides. From part b, we know the sum of the exterior angles of a octagon is
`360^(\circ)`, thus we have
`(360)/(8)=\boxed{45^(\circ)}`