Question

Find the value of angle BACWhat type of triangle is this?

Answer 1

Given:

`\begin{gathered} \Delta ABC \\ m\angle ABC=60^(\circ),m\angle BAC=(5x-40)^(\circ),m\angle ACB=(3x)^(\circ) \end{gathered}`

The sum of all angles of the triangle is 180 degrees.

`\begin{gathered} m\angle ABC+m\angle BAC+m\angle ACB=180^(\circ) \\ 60^(\circ)+(5x-40)^(\circ)+(3x)^(\circ)=180^(\circ) \\ 8x+20=180 \\ 8x=160 \\ x=20 \end{gathered}`

It gives,

`\begin{gathered} m\angle BAC=(5x-40)^(\circ)=(5\cdot20-40)^(\circ)=60^(\circ) \\ m\angle ACB=(3x)^(\circ)=(3\cdot20)^(\circ)=60^(\circ) \end{gathered}`

As all the measure of the angles of a given triangle is equal that is 60 degrees. So, It is the equilateral triangle.

Answer:

`\begin{gathered} m\angle BAC=60^(\circ) \\ \text{Type: an equilateral triangle} \end{gathered}`