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# need help asap

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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
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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)   Dec 4, 2020
#2
+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°   Dec 4, 2020
#3
+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   Dec 4, 2020