Identify the Triangle Type: Analysis of 60° Angle Properties

Let's remember that the sum of angles in a triangle equals 180 degrees.

Let's calculate alpha in the following way:

$60+\alpha+\frac{\alpha}{2}=180$

$60+1\frac{1}{2}\alpha=180$

$1\frac{1}{2}\alpha=180-60$

$1\frac{1}{2}\alpha=120$

Let's divide both sides by 1.5:

$\alpha=80$

Now we can calculate the remaining angle in the triangle:

$\frac{\alpha}{2}=\frac{80}{2}=40$

So in the triangle we have 3 angles: 60, 80, 40

All of them are less than 90 degrees, therefore all angles are acute angles and the triangle is an acute triangle.