A hexagon is inscribed in a circle:
What is the measure of \(\alpha\), in degrees?
the figure is cyclic, so those three angles are just half of the total sum of all the angles, which is 720/2. subtracting, you get 360-105-110=145.
HOPE THIS HELPED!
Join the alpha vertex to the vertex opposite and then you have two cyclic quads. (one on top and one underneath)
So alpha is the sum of (180-105)+(180-110) = 75+70=145 degrees
I know this is the same as asad's answer, it is just another way of doing it (I actually did not understand asad's method.)
Thanks asdf and Melody......here's another way to look at this....but not as nice as yours....!!!
The 110° angle intercepts a major arc of 220°......so the minor arc that it subtends = 360 - 220 = 140°
The 105° angle subtends a major arc of 210° ......so the minor arc it subtends = 360 - 210 = 150°
So.....this means that the minor arc subtended by "a" must be 360 - 140 - 150 = 70°
So.....the major arc it intercepts = 360 - 70 = 290°
So....its measure is 1/2 of this = 145°