Answer-
[tex]\boxed{\boxed{m\angle ACB=45^{\circ}}}[/tex]
Solution-
The octagon in the figure is equiangular, i.e the octagon is a regular octagon.
So the octagon has 8 equal sides and 8 equal interior angles.
The sum of all of the interior angles is [tex](n-2)180=6\times 180=1080^{\circ}[/tex]
Measurement of each interior angle is,
[tex]\dfrac{1080}{8}=135^{\circ}[/tex]
∠ABC is the exterior angle of the octagon.
The interior and exterior angles are complimentary, so
[tex]\Rightarrow 135^{\circ}+m\angle ABC=180^{\circ}[/tex]
[tex]\Rightarrow m\angle ABC=180^{\circ}-135^{\circ}[/tex]
[tex]\Rightarrow m\angle ABC=45^{\circ}[/tex]
As, in ΔABC AB = AC, so
[tex]\Rightarrow m\angle ABC=m\angle ACB[/tex]
[tex]\Rightarrow m\angle ABC=m\angle ACB=45^{\circ}[/tex]
