The angles of a triangle are in arithmetic progression. Prove that the triangle has the angle of 60 deg.

We know that the sum of measures of the angles of a
triangle is 180 degrees.

We'll note the angles of the
triangle as a,b,c.

We also know that the angles of the
triangle are the terms of an a.p.

So, we can write the
angles as:

b = a + d

c = b +
d

d is the common difference of the arithmetic
progression.

The sum of the angles is 180
degrees.

a + b + c = 180

We'll
substitute  b and c by the relations above.

a + a + d + a +
d + d = 180

We'll combine like
terms:

3a + 3d = 180
degrees.

We'll factorize by
3:

3(a + d) = 180

We'll divide
by 3:

a + d = 60

But a + d is
the measure of the angle b, so the angle b is of 60
degrees.

a + d = b =  60
degrees