Question

Please help.

Answer 1

The sum of the measures of the interior angles of a regular octagon equal 1080. Each angle equals 1080/8 = 135
The interior angle B = 135 so it's supplement (angle ABC) = 45 degrees. Since AB = AC, triangle ABC is isosceles, therefore angle ACB also equals 45 degrees.
Letter B

Answer 2

Answer-

$\boxed{\boxed{m\angle ACB=45^{\circ}}}$

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 $(n-2)180=6\times 180=1080^{\circ}$

Measurement of each interior angle is,

$\dfrac{1080}{8}=135^{\circ}$

∠ABC is the exterior angle of the octagon.

The interior and exterior angles are complimentary, so

$\Rightarrow 135^{\circ}+m\angle ABC=180^{\circ}$

$\Rightarrow m\angle ABC=180^{\circ}-135^{\circ}$

$\Rightarrow m\angle ABC=45^{\circ}$

As, in ΔABC AB = AC, so

$\Rightarrow m\angle ABC=m\angle ACB$

$\Rightarrow m\angle ABC=m\angle ACB=45^{\circ}$