Question

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

विकल्प

• 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^circ`  ...[∵ Equation (i) is divided by 2]

⇒ `1/2 (∠B + ∠C) = 35^circ`

Now, in ΔBOC,

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

⇒ `∠BOC + 1/2 (∠B + ∠C) = 180^circ`  ...[∵ 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°