The figure above is a regular octagon with radii and an apothem drawn. What is m∠1, m∠2?

Solution:

Since it is a regular polygon the exterior angle will be given 360°/n. Since the octagon has eight sides the exterior angle will be :

m∠1 = 360°/8 = 45°

Hence the interior angle will be 180° - 45° = 135°

Since it is a regular octagon and everything is symmetrical in the figure above

m∠2 = 135°/2 = 67.5° 

The figure above is a regular octagon with radii and an apothem drawn. What is m∠1, m∠2?

Summary:

The figure which is a regular octagon with radii and has an apothem drawn the value of m∠1 and m∠2 are  45° and 67.5° respectively