We will label the base angles of the triangle as "x".
[tex]\text{Base angle=x}[/tex]Since the vertex angle is 3 times the measure of the base angle, the vertex angle will be equal to 3x:
[tex]\text{Vertex angle =3x}[/tex]The following image represent the angles in the isosceles triangle:
Now we use the following property of triangles:
The sum of all of the internal angles in a triangle must be equal to 180°.
Thus, we add the angles and equal them to 180°
[tex]3x+x+x=180[/tex]We combine the terms on the left:
[tex]5x=180[/tex]And divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{180}{5} \\ x=36 \end{gathered}[/tex]And since x=36, the vertex angle will be:
[tex]\text{vertex angle = 3x = 3(36)=108\degree}[/tex]answer: 108°
