Question

Can somebody help me with this question

Answer 1

Answer:

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

Step-by-step 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 $\frac{1080}{8}=\boxed{135^{\circ}}$

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 $\frac{360}{8}=\boxed{45^{\circ}}$