+0  
 
0
170
2
avatar

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)

 Jul 29, 2019
 #1
avatar+792 
+3

\(\angle\)

from latex enter \ angle

 Jul 29, 2019
 #2
avatar+106536 
+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°

 

 

cool cool cool

 Jul 29, 2019

5 Online Users