Question

Need to know the following angle

Answer 1

Given:

`m\angle A=(2x-15)^\circ`

`m\angle B=(x-5)^\circ`

`\text{Exterior}\ m\angle C=148^\circ`

To find:

The
`m\angle ABC`.

Solution:

In triangle ABC,

`\text{Exterior}\ m\angle C=m\angle A+m\angle B` [Exterior angle theorem]

`148=(2x-15)+(x-5)`

`148=3x-20`

`148+20=3x`

`168=3x`

Divide both sides by 3.

`(168)/(3)=x`

`56=x`

Now,

`m\angle ABC=(x-5)^\circ`

`m\angle ABC=(56-5)^\circ`

`m\angle ABC=51^\circ`

Therefore,
`m\angle ABC=51^\circ`.