Question

If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be ______.

विकल्प

• 50°

• 65°

• 145°

• 155°

Answer 1

If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be 155°.

Explanation:

Let angles of a triangle be ∠A, ∠B and ∠C.

In ΔABC,

∠A + ∠B +∠C = 180°   ...[Sum of all interior angles of a triangle is 180°]

⇒ `1/2 ∠A + 1/2 ∠B + 1/2 ∠C = (180^circ)/2 = 90^circ`  ...[Dividing both sides by 2]

⇒ `1/2 ∠B + 1/2 ∠C = 90^circ - 1/2 ∠A`  ...[∵ In ΔOBC, ∠OBC + ∠BCO + ∠COB = 180°]

`["Since", (∠B)/2 + (∠C)/2 + ∠BOC = 180^circ  "as"  BO and OC  "are the angle bisectors of"  ∠ABC  "and"  ∠BCA,  "respectively"]`

⇒ `180^circ - ∠BOC = 90^circ - 1/2 ∠A`

∴ `∠BOC = 180^circ - 90^circ + 1/2 ∠A`

= `90^circ + 1/2 ∠A`

= `90^circ + 1/2 xx 130^circ`  ...[∴ ∠A = 130° (given)]

= 90° + 65°  

⇒ 155°

Hence, the required angle is 155°.