Question

The one of the angle triangle is 126° then the angle between the two bisectors of the other two angles is​

Answer 1

Given:

ABC is a triangle.

OB is the bisector of ∠ABC, i.e  ∠ABC= 2∠OBC...............(1)

OC is the bisector of ∠ACB, i.e. ∠ACB= 2∠OCB............(2)

∠BAC=126°

To Find:

Find  ∠BOC

Solution:

In triangle ABC,

∠BAC+ ∠ACB+ ∠ABC=180°

126°+ 2∠OCB+ 2∠OBC=180°(from eq1 and eq2)

∠OCB+∠OBC=$\frac{1}{2} (180-126)$

∠OCB+∠OBC=27°...............................(3)

In triangle OBC,

∠BOC+∠OCB+∠OBC=180°

∠BOC+27°=180°

∠BOC=153°

Hence the angle between the two bisectors of other two angles is 153°.

Answer 2

Answer:

The angle between the two bisectors of the two angles is 153°.

Angle Bisector:

• Angle bisector is a segment that divides the angle into two equal parts.
• The angle bisector divides the side opposite to the angle into two parts proportional to the adjacent sides.
• The ratio of one part of the divided side to its adjacent side is equal to the ratio of the other part of the divided side to its adjacent side.

Step-by-step explanation:

Segments AO and CO are the two angle bisectors of ∠BAC and ∠BCA. The angle between the two bisectors is ∠AOC.

Given:

∠ABC = 126°

To find:

∠AOC

Step 1:

The angle bisector divides the angle into two equal parts. Therefore,

∠BAC = ∠BAO + ∠CAO

∠BAC = 2∠CAO ...(i)

Similarly,

∠BCA = ∠BCO + ∠ACO

∠BCA = 2∠ACO ...(ii)

Step 2:

We know that the sum of the angles of a triangle adds up to 180°.

In ΔABC,

∠ABC + ∠BAC + ∠BCA = 180°

126° + ∠BAC + ∠BCA = 180°

∠BAC + ∠BCA = 180 - 126

∠BAC + ∠BCA = 54° ...(iii)

Step 3:

Substituting equations (i) and (ii) in equation (iii)

2∠CAO + 2∠ACO =  54°

2(∠CAO + ∠ACO) = 54°

∠CAO + ∠ACO = 27° ...(iv)

Step 4:

We know that the sum of the angles of a triangle adds up to 180°.

In ΔAOC,

∠AOC + ∠CAO + ∠ACO = 180°

From equation (iv), we get

∠AOC + 27° = 180°

∠AOC = 180 - 27

∠AOC = 153°

Therefore, the angle between the bisectors is 153°.

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