please give solution Q) In the figure, BO and CO are bisectors of ∠B and ∠C and respectively, find - Maths - Lines and Angles

Question

please give solution
Q) In the figure, BO and CO are bisectors of ∠ B   a n d
  ∠ C and respectively, find the value ∠ B O C

Varun Rawat · Accepted Answer

Let ∠ABC = x and ∠ACB = yIn ∆ABC,∠BAC + ∠ABC + ∠ACB = 180°  Angle sum property⇒50° + x + y = 180°⇒x + y = 130°Now, OB bisects ∠CBE and OC bisects ∠BCD
Now, ∠CBO = 12∠CBE  and  ∠BCO = 12∠BCDNow, ∠ABC + ∠CBE = 180°  Linear pair⇒x + 2∠CBO = 180°⇒∠CBO = 180° - x2Now, ∠ACB + ∠BCD = 180°   Linear pair⇒y + 2∠BCO = 180°⇒∠BCO= 180° - y2Now, in ∆BOC,∠BOC + ∠CBO + ∠BCO = 180°  Angle sum property⇒∠BOC + 180° - x2 + 180° - y2 = 180°⇒2∠BOC + 180° - x + 180° - y = 360°⇒∠BOC = x+y2 = 130°2 = 65°

please give solution Q). In the figure, BO and CO are bisectors of ∠ B a n d ∠ C and respectively, find the value ∠ B O C .

please give solution
Q). In the figure, BO and CO are bisectors of $∠ B a n d ∠ C$ and respectively, find the value $∠ B O C$ .