Question
Find the value of x if BO and OC are angle bisectors of angle B and C respectively
- 90°
- 130°
- 145°
- 55°
Hint:
Using sum of angles in a triangle property and angular bisector divides the angle in to two equal parts .Find the value of x
The correct answer is: 130°
In ∆ ABC, ∠BAC + ∠ABC + ∠ACB = 180° (Angle Sum property of triangle)
⇒ 80° + ∠B + ∠C = 180°
⇒ ∠B + ∠C = 100° ————- (i)
Also, In ∆ BOC, ∠BOC + ∠OBC + ∠OCB = 180° (Angle Sum property of triangle)
⇒ ∠BOC + 1/2 ∠B + 1/2 ∠C = 180° (BO and OC are angle bisectors)
⇒ ∠BOC + 1/2 (∠B + ∠C) = 180°
⇒ ∠BOC + 1/2 (100°) = 180° (from equation i)
⇒ ∠BOC = 180° – 50°
⇒ ∠BOC = 130°.
Therefore, value of x is 130°.
⇒ 80° + ∠B + ∠C = 180°
⇒ ∠B + ∠C = 100° ————- (i)
Also, In ∆ BOC, ∠BOC + ∠OBC + ∠OCB = 180° (Angle Sum property of triangle)
⇒ ∠BOC + 1/2 ∠B + 1/2 ∠C = 180° (BO and OC are angle bisectors)
⇒ ∠BOC + 1/2 (∠B + ∠C) = 180°
⇒ ∠BOC + 1/2 (100°) = 180° (from equation i)
⇒ ∠BOC = 180° – 50°
⇒ ∠BOC = 130°.
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