Given regular pentagon ABCDE a circle can be drawn that is tangent to DE at D and to AB at A. In degrees, what is the measure of minor arc AD?

Lightning Jan 13, 2019

#2**+1 **

Let us let the center of the circle be at F

Drawing radii from F to both D and A will result in right angles CDF and BAF

And ABCDF will form an irregular pentagon.....the sum of the interior angles of this pentagon = 540°

Angles DCB and ABC = 108°

So....we can find angle AFD as

540 - 108 - 108 - 90 - 90 = 144°

But AFD is a central angle in the circle....so....its measure = minor arc AD = 144°

CPhill Jan 13, 2019