1 Answer

Watcom · Answer 1 · 2019-12-02T17:14:50+0000

Look at the picture.

$\alpha=(360^o)/(8)=45^o$

We know: The sum of measures of interior angles in the triangle is equal 180°.

Therefore:

$\alpha+2\beta=180^o\\\\45^o+2\beta=180^o\ \ \ |-45^o\\\\2\beta=135^o$

When we add up the Interior Angle and Exterior Angle we get a straight line 180°. They are "Supplementary Angles".

$\gamma=180^o-2\beta\to\gamma=180^o-135^o=45^o$

Answer: The measure of an exterior angle of a regular oktagon is equal 45°.

Please log in or register to add a comment.