SOLUTION: triangle ABC is inscribed in a circle. given that AB is a 40 degree arc and ABC is a 50 degree angle, find the sizes of the other arcs and angles in the figure. thankyou:]

Angle ACB is an inscribed angle, subtending a 40° arc.
An inscribed angle has  the measure of its inscribed arc.
Therefore angle ACB has measure 20°, so we write that in:



Since the three angles of any triangle total 180°, we find the 
remaining angle BAC by adding 50°+20°, getting 70°, then subtracting
from 180° and getting 110°, so we write that in for angle BAC:



The inscribed angle at B is 50°. It subtends arc AC, and since it 
is  of the measure of its inscribed arc, the arc AC must be
2x50° or 100°, so we write in 100° for arc AC:



The big major arc going clockwise from B around to C is subtended by 
the 110° angle at A.  And since it is  of the measure of its 
inscribed arc, the large major arc BC must be 2x110° or 220°, so we 
write in 220° for major arc BC, going clockwise from B around to C:



Notice as a partial check that the three arcs have sum 360°.

minor are AB =  40²
minor arc AC = 100°
major arc BC = 220°
-------------------
       total = 360°

Edwin