Certainly! Let's solve the problem step-by-step:
1. Understanding Isosceles Triangles:
- An isosceles triangle has at least two sides that are of equal length.
- The angles opposite the equal sides are also equal. These are called the base angles.
2. Given Information:
- The base angle of the isosceles triangle measures 54°.
3. Sum of Angles in a Triangle:
- We know that the sum of all interior angles in any triangle is 180°.
4. Identify the Base Angles:
- Since the triangle is isosceles and one base angle is 54°, the other base angle is also 54° (because base angles in an isosceles triangle are equal).
5. Calculate Total of the Base Angles:
- Total measure of the two base angles = 54° + 54° = 108°.
6. Find the Measure of the Vertex Angle:
- To find the vertex angle, subtract the total measure of the base angles from the sum of the angles in the triangle.
- Vertex angle = 180° - 108° = 72°.
Thus, the measure of the vertex angle in the given isosceles triangle is 72°.
