In an isosceles triangle, two sides are of equal length, and the angles opposite those sides are equal as well. When you know the measure of the vertex angle, you can easily find the measure of the base angles using the properties of triangles.
The sum of the angles in any triangle is always 180 degrees. In our case, we have one vertex angle measuring 84 degrees. Let’s denote the measure of each base angle as x.
The equation representing the sum of the angles in the triangle is:
84 + x + x = 180
Simplifying this equation:
84 + 2x = 180
Now, isolate 2x:
2x = 180 - 84
2x = 96
Next, divide both sides by 2 to solve for x:
x = 96 / 2
x = 48
Thus, the measure of each base angle in the isosceles triangle is 48 degrees.