Question

BD is the angle bisector of

Answer 1

Note: Let us consider, we need to find the
`m\angle ABC` and
`m\angle DBC`.

Given:

In the given figure, BD is the angle bisector of ABC.

To find:

The
`m\angle ABC` and
`m\angle DBC`.

Solution:

BD is the angle bisector of ABC. So,

`m\angle ABD=m\angle DBC`

`3x=x+20`

`3x-x=20`

`2x=20`

Divide both sides by 2.

`x=(20)/(2)`

`x=10`

Now,

`m\angle DBC=(x+20)^\circ`

`m\angle DBC=(10+20)^\circ`

`m\angle DBC=30^\circ`

And,

`m\angle ABC=(3x)^\circ+(x+20)^\circ`

`m\angle ABC=(4x+20)^\circ`

`m\angle ABC=(4(10)+20)^\circ`

`m\angle ABC=(40+20)^\circ`

`m\angle ABC=60^\circ`

Therefore,
`m\angle DBC=30^\circ,m\angle ABD=30^\circ` and
`m\angle ABC=60^\circ`.