A regular and an irregular octagon both have 8 interior angles
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The two similar shapes will have the same angles
Some shapes have angles and so they are important in defining the shapes. And angles are absolutely critical for angles. They are the very essence of their existence: if it were not for angles then there would be no angles.
Supplementary angles do not have to be next to one another but, they can be parts of two different shapes.
In short, no. Similar shapes are shapes in which all corresponding angles congruent regardless of the length of the sides. Congruent shapes have congruent corresponding angles and corresponding sides. In effect congruent shapes is a special condition of similar shapes.
If there are two 90 degree angles on the shape (example: squares or rectangles' corners)