Look at the picture.
[tex]\alpha=\dfrac{360^o}{8}=45^o[/tex]
We know: The sum of measures of interior angles in the triangle is equal 180°.
Therefore:
[tex]\alpha+2\beta=180^o\\\\45^o+2\beta=180^o\ \ \ |-45^o\\\\2\beta=135^o[/tex]
When we add up the Interior Angle and Exterior Angle we get a straight line 180°. They are "Supplementary Angles".
[tex]\gamma=180^o-2\beta\to\gamma=180^o-135^o=45^o[/tex]
Answer: The measure of an exterior angle of a regular oktagon is equal 45°.
