We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
82
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+773 
+3

\(\angle\)

from latex enter \ angle

 Jul 29, 2019
 #2
avatar+103148 
+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

10 Online Users

avatar