The sum of the interior angles of any triangle is always 180°.
For the given right triangle:
[tex]m\angle2+m\angle3+90=180[/tex]
Use the given meauste for triangles 2 and 3:
[tex](x+8)+(2x+7)+90=180[/tex]
Solve the equation above for x:
[tex]\begin{gathered} x+8+2x+7+90=180 \\ 3x+105=180 \\ \\ \text{Subtract 105 in both sides of the equation:} \\ 3x+105-105=180-105 \\ 3x=75 \\ \\ \text{Divide both sides of the equation into 3:} \\ \frac{3}{3}x=\frac{75}{3} \\ \\ x=25 \end{gathered}[/tex]
Use the value of x=25 to find the measure of angle 2:
[tex]\begin{gathered} m\angle2=x+8 \\ m\angle2=25+8 \\ m\angle2=33 \end{gathered}[/tex]Then, the measure of angle 2 is 33°
