A circle is circumscribed around ABCD as follows:
image:
https://latex.artofproblemsolving.com/5/d/e/5de53ded144abd0a73f43e0d25b064d2a0221598.png
How many degrees are in angle CAB + angle ACD?
(sry i didnt know how to do the angle sign)
+128448 Note that angle CAD = 30°
Since this an inscribed angle.....then the measure of minor arc CD is twice this = 60°
And angle ACB = 40°
Then......by simiar reasoning.....minor arc AB = 80°
Then the sum of of the measures of minor arcs AD and BC must be 360 - 60 - 80 = 360 - 140 = 220°
But these arcs are intercepted by angles ACD and CAB
So.....the sum of their measures must = (1/2) of the sum of these arcs = (1/2)(220°) = 110°
