In an isosceles triangle, there are two equal angles known as base angles and one angle known as the vertex angle. In this case, each base angle measures 54 degrees.
To find the vertex angle, we can use the property that the sum of all angles in a triangle equals 180 degrees. Hence, we can set up the following equation:
Vertex Angle + Base Angle + Base Angle = 180 degrees
Substituting the known values into the equation:
Vertex Angle + 54 + 54 = 180
Now, simplifying this gives:
Vertex Angle + 108 = 180
Next, we subtract 108 from both sides:
Vertex Angle = 180 – 108
When we calculate that, we find:
Vertex Angle = 72 degrees
So, the measure of the vertex angle in the isosceles triangle is 72 degrees.