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Lines AB and CD intersect at a point O in such a way that ∠DOB = 4∠COB. What is ∠AOD? 

 

In 4ABC, AB = AC and ∠A = 72◦ . What is ∠B?

 

O is the circumcenter of 4ABC. If OB = OC = BC, what is ∠BAC?

 Dec 4, 2020
 #1
avatar+114592 
+2

Lines AB and CD intersect at a point O in such a way that ∠DOB = 4∠COB. What is ∠AOD? 

 

A                C

 

 

         O

 

D                 B

 

DOB + COB   =180

Then

4COB + COB  =180

5COB  =180

COB = 180/5  = 36

 

And AOD  is  the vertical angle to COB......so AOD  also  = 36  (degrees)

 

 

 

cool cool cool

 Dec 4, 2020
 #2
avatar+114592 
+2

In ΔABC, AB = AC and ∠A = 72◦ . What is ∠B?

 

                          A

 

 

                B                    C

 

Since  AB  = AC   then  angles  B  and C  are equal

 

So     B =   (180  - 72)   / 2  =      108/2  =   54°

 

cool cool cool

 Dec 4, 2020
 #3
avatar+114592 
+2

 

O is the circumcenter of ΔABC. If OB = OC = BC, what is ∠BAC?

 

 

                                       A

 

                                      

                                      O

 

                         B                      C

 

If OB = OC  = BC, then triangle  BOC   is equilateral  with central angle  BOC =  60

 

And angle BAC   is an inscribed angle  subtending  the  same arc as  BC.....so.....its measure  = 1/2  BOC  = 

30

 

cool cool cool

 Dec 4, 2020

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