-
∆ABC is isosceles having AB = AC and ∠A = 40°. Bisectors PO and OQ of the exterior angles ∠ABD and &Ang;ACE formed by producing BC on both sides, meet at O. Then the value of ∠BOC is
-
- 70°
- 110°
- 80°
- 55°
- 70°
Correct Option: A
On the basis of given in question , we draw a figure of an isosceles triangle ABC which bisectors PO and OQ of the exterior angles ∠ABD and &Ang;ACE formed by producing BC on both sides, meet at O
Given , AB = AC
∴ ∠ABC = ∠ACB = 140 ÷ 2 = 70°
∴ ∠ABD = ∠ACE = 180° - 70° = 110°
∴ ∠PBD = 55° = ∠CBO
∠QCE = ∠BCO = 55°
&there4 ∠BOC = 180° – 2 × 55° = 180° – 110° = 70°
