If o is the centre of the circle angle ABO=50 degree and angle ACO=20 degree find the measure of angle BOC.
 

I n   f i g u r e ,   i f   O   i s   t h e   c e n t r e   o f   t h e   c i r c l e ,   A B O   =   50 °   a n d   A C O   =   20 ° ,   f i n d   t h e   m e a s u r e   o f   B O C .

 

given  AOC =20 ,ABO =50
SO AOC+BOC+ABO=180(LINEAR PAIR AXIOM)
20+BOC+50=180
BOC=180-70
BOC=110
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Given that 
∠ACO=20°, ∠ABO=50°
∠BOC + ∠ACO + ∠ABO =180° (Linear Pair)
∠BOC +   20°  +   50° = 180°
∠BOC +   70°= 180°
∠BOC = 180° - 70° = 110°
∠BOC=110°

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