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,
[tex]x+y+z=180^{\circ}[/tex]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,
[tex]y+z=3x[/tex]Subsititute y+z=3x in the equation x+y+z=180,
[tex]\begin{gathered} x+y+z=180^{\circ} \\ x+3x=180^{\circ} \\ 4x=180^{\circ} \\ x=\frac{180}{4} \end{gathered}[/tex]So by furthur simplifying the value of x can be founded,
[tex]\begin{gathered} x=\frac{180}{4} \\ x=45 \end{gathered}[/tex]The value of x is 45 degree.
Subsitute the value of x in the equation y+z=3x. we get,
[tex]\begin{gathered} y+z=3x \\ y+z=3\times45 \\ y+z=135 \end{gathered}[/tex]By the given condition "The third angle is 29 more than the second". It is clear that,
[tex]z=29+y[/tex]Subsititute the equation z=29+y in the equation y+z=135,
[tex]\begin{gathered} y+z=135 \\ y+29+y=135 \\ 2y+29=135 \\ 2y=135-29 \\ 2y=106^{\circ} \\ y=53^{\circ} \end{gathered}[/tex]The value of y is 53 degree.
Subsitute the value of x and y in the equation x+y+z=180. We get,
[tex]\begin{gathered} x+y+z=180^{\circ} \\ 45+53+z=180 \\ 98+z=180 \\ z=180-98 \\ z=82^{\circ} \end{gathered}[/tex]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,
[tex]x=45^{\circ},y=53^{\circ},z=82^{\circ}[/tex]