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)

Guest Jul 29, 2019

#2**+1 **

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°

CPhill Jul 29, 2019