Question

I am trying to figure out how to assign the variables and set up the equation.

Answer 1

Let the three angles be x,y,z.

By the Given conditon "The sum of the measures of the angles of a triangle is 180". It is clear that,

`x+y+z=180^(\circ)`

By the given conditon " The sum of the measures of the second and third angles is three times the measure of the first angle". It is clear that,

`y+z=3x`

Subsititute y+z=3x in the equation x+y+z=180,

`\begin{gathered} x+y+z=180^(\circ) \\ x+3x=180^(\circ) \\ 4x=180^(\circ) \\ x=(180)/(4) \end{gathered}`

So by furthur simplifying the value of x can be founded,

`\begin{gathered} x=(180)/(4) \\ x=45 \end{gathered}`

The value of x is 45 degree.

Subsitute the value of x in the equation y+z=3x. we get,

`\begin{gathered} y+z=3x \\ y+z=3*45 \\ y+z=135 \end{gathered}`

By the given condition "The third angle is 29 more than the second". It is clear that,

`z=29+y`

Subsititute the equation z=29+y in the equation y+z=135,

`\begin{gathered} y+z=135 \\ y+29+y=135 \\ 2y+29=135 \\ 2y=135-29 \\ 2y=106^(\circ) \\ y=53^(\circ) \end{gathered}`

The value of y is 53 degree.

Subsitute the value of x and y in the equation x+y+z=180. We get,

`\begin{gathered} x+y+z=180^(\circ) \\ 45+53+z=180 \\ 98+z=180 \\ z=180-98 \\ z=82^(\circ) \end{gathered}`

The value of z is 82 degree.

So the value of x is 45 degree, the value of y is 53 degree and the value of z is 82 degree. That is,

`x=45^(\circ),y=53^(\circ),z=82^(\circ)`