An isosceles triangle has two equal angles and one different angle. The angle that is different is called the vertex angle.
We can see in the following image a representation of this problem:
The vertex angle is at the top, the two angles marked in yellow have to be equal because it is an isosceles triangle.
The vertex angle is 64° and we will call the yellow angles x:
Now, we use the following property of triangles:
• The sum of all of the angles inside a triangle is 180°
So we need to add the angles in the triangle of this problem and equal them to 180°:
[tex]x+x+64=180[/tex]Now we solve this equation for x. First, we add the like terms:
[tex]2x+64=180[/tex]Now, subtract 64 to both sides:
[tex]\begin{gathered} 2x=180-64 \\ 2x=116 \end{gathered}[/tex]Next, divide both sides by 2:
[tex]\begin{gathered} x=\frac{116}{2} \\ x=58 \end{gathered}[/tex]The value of x is 58°. (x represents the base angles).
Answer: The measures of the base angles are 58°
