Q34 of 153 Page 148

In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 50°, then ∠BOC = ?

In ∆ABC,


∠A + ∠B + ∠C=180°


50° + ∠B + ∠C=180°


∠B + ∠C=180°−50°=130°


∠B = 65°


∠C = 65°


Now in ∆OBC,


∠OBC + ∠OCB + ∠BOC=180°


∠BOC = 180° – 65° (∠OBC + ∠OCB = 65 because O is bisector of ∠B and ∠C)


= 115°

More from this chapter

All 153 →
32

In the given figure, ∠BAC = 30°, ∠ABC = 50° and ∠CDE = 40°. Then ∠AED = ?

 33

In the given figure, ∠BAC = 40°, ∠ACB = 90° and ∠BED = 100°. Then ∠BDE = ?

 35

In the given figure, AB || CD. If ∠EAB = 50° and ∠ECD = 60°, then ∠AEB = ?

 36

In the given figure, ∠OAB = 75°, ∠OBA = 55° and ∠OCD = 100°. Then ∠ODC = ?