Question

If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is ______.

पर्याय

• 70°

• 110°

• 35°

• 145°

Answer 1

If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is 145°.

Explanation:

In ΔABC, ∠A = 110°  .....[Given]

We know that, ∠A + ∠B + ∠C = 180°  ......[Angle sum property of a triangle]

⇒ ∠B + ∠C = 180° – ∠A

⇒ ∠B + ∠C = 180° – 110°

⇒ ∠B + ∠C = 70°  ......(i)

⇒ `1/2 ∠B + 1/2 ∠C = 70/2` = 35°  ......[∵ Equation (i) is divided by 2]

⇒ `1/2 (∠B + ∠C)` = 35°

Now, In ΔBOC,

∠BOC + ∠OBC + ∠OCB = 180°  [Angle sum property of a triangle]  ......(ii)

⇒ `∠BOC + 1/2 (∠B + ∠C)` = 180°  ......[∵ OB and OC are the bisectors of ∠B and ∠C, then ∠OBC = `1/2`∠B and ∠OCB = `1/2`∠C]

⇒ ∠BOC + 35° = 180°

⇒ ∠BOC = 180° – 35°

⇒ ∠BOC = 145°