We have that the measurement of three angles of a triangle is:
1. Angle 1: 2x degrees.
2. Angle 2: 3x degrees.
3. Angle 3: (x+30) degrees.
We know that the sum of the internal angles of a triangle is equal to 180.
Therefore, to find the value of x, we can proceed as follows:
[tex]\begin{gathered} m\angle1+m\angle2+m\angle3=180^{\circ} \\ \\ 2x+3x+(x+30)=180^{\circ} \end{gathered}[/tex]Now, we can add the like terms as follows:
[tex]\begin{gathered} 2x+3x+x+30^{\circ}=180^{\circ} \\ \\ 5x+x+30^{\circ}=180^{\circ} \\ \\ 6x+30^^{\circ}=180^{\circ} \end{gathered}[/tex]We can subtract 30 degrees to both sides of the equation, and then we have to divide both sides by 6:
[tex]\begin{gathered} 6x+30^{\circ}-30^{\circ}=180^{\circ}-30^{\circ} \\ \\ 6x=150^^{\circ} \\ \\ \frac{6x}{6}=\frac{150}{6} \\ \\ x=25 \end{gathered}[/tex]Therefore, in summary, the value for x is equal to 25.
