Question

In the given figure angle a=40 if bo and co are bisectors of angle b and angle c respectively find the measure of angle boc

Answer 1

Answer:

• ∠BOC = 110°

Step-by-step explanation:

Given

• ∠A = 40°
• BO and CO are the bisectors of ∠B and ∠C

To find

• ∠BOC

Solution

We know that BO is the bisector of ∠B and CO is the bisector of ∠C,

Let ∠CBO = ABO = x°

and ∠BCO = ∠ACO = y°

Then, ∠B = 2x°

and ∠C = 2y° and ∠A = 40°

Now, according to angle sum property:

• ∠A + ∠B + ∠C = 180°
• 2x° + 2y° + 40° = 180°
• 2(x + y)° = 140°
• x° + y° = 140°/2
• x° + y° = 70°

Hence, ∠BOC = 180° - 70° = 110°