Question

In AVWX, m_V = (6x – 4)', m_W = (a + 12), and m_X = (3x + 2)°.Find m_W.

Answer 1

As per given by the question,

There are given that a triangle, triangle VWX.

Now,

There are also given that the angles of triangle,

`\begin{gathered} m\angle V=(6x-4)^(\circ) \\ m\angle W=(x+12)^(\circ) \\ m\angle X=(3x+2)^(\circ) \end{gathered}`

Then,

According to the properties of the triangle;

The total sum of the angles are equal to 180 degree.

So,

From the given angles of the triangle VWX,

`m\angle V+m\angle W+m\angle X=180^(\circ)`

Put the value of all angles into above properties.

Then,

`\begin{gathered} m\angle V+m\angle W+m\angle X=180^(\circ) \\ (6x-4)^(\circ)+(x+12)^(\circ)+(3x+2)^(\circ)=180^(\circ) \end{gathered}`

Solve the above equation to get the value of x,

`\begin{gathered} (6x-4)^(\circ)+(x+12)^(\circ)+(3x+2)^(\circ)=180^(\circ) \\ 6x-4+x+12+3x+2=180 \\ 10x+10=180 \\ 10x=180-10 \\ 10x=170 \\ x=17 \end{gathered}`

Now,

If value of x is 17, then find the measure of angle W,

So,

Put the value of x into the angle W,

Then,

`\begin{gathered} m\angle W=(x+12)^(\circ) \\ m\angle W=(17+12)^(\circ) \\ m\angle W=29^(\circ) \end{gathered}`

Hence, the value of measure angle W is 29 degree.