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

Question

Philoid · Accepted Answer

The figure for the given question is –

We have a ΔABC.

Let one of the angles of the triangle,

Let CP and BQ be the bisectors of ∠C and ∠B respectively.

Let us denote the intersection of the two bisectors, CP and BQ as D.

We have to find ∠BDC.

We know the sum of all the angles of a triangle is 180°.

So, in ΔABC,

Let us divide both the sides by 2. Then, the equation becomes

⇒ - - - - (i)

Now, in ΔBDC,

⇒

⇒ - - - - (ii)

Substituting equation (ii) in equation (i), we get

⇒

⇒ (Since ∠A = 130°)

⇒

Hence, the angle between the bisectors of the two angles, i.e., ∠CDB is 155°.

Option (A) is not correct because

- - - - (iii)

Since the sum of all the angles of a triangle is 180°.

⇒

⇒ (Since ∠A = 130°)

⇒ - - - - (iv)

From equation (iii) and equation (iv),

We find that the angle between the bisectors of the two angles is not .

So, the angle between the bisectors of the two angles is not 50°.

Option (B) is not correct because

⇒

This is not the angle between the bisectors of the two angles.

Option (C) is not correct because this is not the correct angle between the bisectors of the two angles.