Question

In TRIANGLE ABC, what is the value of x?

Answer 1

Answer:
`70^(\circ)`

Explanation:

Given

`\angle BAC=112^(\circ)\\\angle BCM=(2x+12)^(\circ)\\\angle ABL=2x^(\circ)`

`\angle ACB` is given by
`180^(\circ)-\angle BCM` as the angle around a straight line is
`180^(\circ)`

`\therefore \angle BCA=180^(\circ)-2x^(\circ)-12^(\circ)\\\angle BCA=(168-2x)^(\circ)`

Also, using exterior angle property. We can write

`\angle BCA+\angle BAC=\angle ABL`

Insert the values

`\Rightarrow 168^(\circ)-2x^(\circ)+112^(\circ)=2x^(\circ)\\\Rightarrow 280=4x^(\circ)\\\Rightarrow x=70^(\circ)`