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Given: circle k(O), DC∥AB,AC ∩ DB=O, m AD=108°

Find: m∠A and m∠AOB

 

 Feb 2, 2021
 #1
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Triangles  AOB  and DOC  are  congruent

 

Then  arc   BC  = arc AD    =108°

 

And   angle CAB  (Angle A)  intercepts  arc  BC.....and it  is an inscribed angle, so  it has 1/2  the  measure of this arc  = 54°

 

And angle B  has  the same measure   since   OA  = OB

 

So  angle AOB  =   180  - 2(54)   =  180  - 108  =  72°

 

 

cool cool cool

 Feb 2, 2021

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