Since triangle, ABC is an isosceles triangle because AB = BC
Then the angles of its base are equal
Since the angles of its bases are <2 and <4, then
[tex]m\angle2=m\angle4[/tex]Since <3 and <4 are vertically opposite angles
Since the vertically opposite angles are equal in measures, then
[tex]m\angle3=m\angle4[/tex]Since measure of <3 = 2x + 12, them
[tex]m\angle4=m\angle2=2x+12[/tex]Since <1 and <2 are linear angles
Since the sum of the measures of the linear angles is 180 degrees, then
[tex]m\angle2+m\angle1=180[/tex]Since m<1 = 5x, then
[tex]\begin{gathered} m\angle1=5x \\ m\angle2=2x+12 \\ 2x+12+5x=180 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (2x+5x)+12=180 \\ 7x+12=180 \end{gathered}[/tex]Subtract 12 from both sides
[tex]\begin{gathered} 7x+12-12=180-12 \\ 7x=168 \end{gathered}[/tex]Divide both sides by 7
[tex]\begin{gathered} \frac{7x}{7}=\frac{168}{7} \\ x=24 \end{gathered}[/tex]Then substitute x by 24 in the measure of <2
[tex]\begin{gathered} m\angle2=2x+12 \\ m\angle2=2(24)+12 \\ m\angle2=48+12 \\ m\angle2=\mathring{60} \end{gathered}[/tex]The measure of angle 2 is 60 degrees
