Question

From the above picture Pl solve correctly and give explanation..
i will like ur answer..
​

Answer 1

Answer:

m∠BOC = 90° + (1/2)∠A

Step-by-step explanation:

Given:- In ΔABC, OB and OC are the bisectors of the angles ∠B and ∠C

To find:- m∠BOC

Proof:-

In ΔABC,

∠A + ∠B + ∠C = 180° [Angle Sum Property of Triangles]

Then,

∠B + ∠C = 180° - ∠A ----- 1

Now, In ΔBOC,

∠OBC = (1/2)∠B [OB is a bisector] ------ 2

∠OCB = (1/2)∠C [OC is a bisector] ------ 3

Also,

∠OBC + ∠OCB + ∠BOC = 180° [Angle Sum Properties of Triangles]

From eq.2 and eq.3 we get,

(1/2)∠B + (1/2)∠C + ∠BOC = 180°

then,

∠BOC = 180° - (1/2)∠B - (1/2)∠C

∠BOC = 180° - ((1/2)∠B + (1/2)∠C)

(1/2) is common So,

∠BOC = 180° - (1/2)(∠B + ∠C)

From eq.1 we get,

∠BOC = 180° - (1/2)(180° - ∠A)

∠BOC = 180° - ((1/2)(180°) - (1/2)∠A)

∠BOC = 180° - (90° - (1/2)∠A)

Opening brackets,

∠BOC = 180° - 90° + (1/2)∠A

∠BOC = 90° + (1/2)∠A

Thus, m∠BOC = 90° + (1/2)∠A

Here m just stands for the 'measure' of the angle.

Hope it helped and you understood it........All the best