In an isosceles triangle, the two base angles are equal. Given that each base angle measures 54 degrees, we can find the vertex angle using the triangle sum theorem, which states that the sum of the angles in a triangle is always 180 degrees.
To find the vertex angle (let’s call it V), we can set up the equation:
2 * (Base Angle) + Vertex Angle = 180°
Substituting in the base angle:
2 * 54° + V = 180°
108° + V = 180°
Now, to isolate V, we subtract 108° from both sides:
V = 180° – 108°
V = 72°
Therefore, the measure of the vertex angle is 72 degrees.