Hi I am slightly stuck on this proof. So before this proof I was asked to prove that if X>Y>Z and the angles form an arithmetic progression prove Y = 60 degrees. I was able to do this, but I am slightly unsure on how to make the reverse work. So this was a method I came up with but I am not sure whether this is right. Can someone please help me clarify this?
So I approached this as follows:
Assume that X < Y < Z and they do follow an arithmetic progression then:
X = a
Y = a + d
Z = a + 2d
the sum of the angles must be 180 degrees so:
a + a + d + a + 2d = 180
3a + 3d = 180
dividing by 3
a + d = 60
since a + d = 60 is Y and that this was stated in the question, it follows that they do follow an arithmetic progression given X < Y < Z
So I approached this as follows:
Assume that X < Y < Z and they do follow an arithmetic progression then:
X = a
Y = a + d
Z = a + 2d
the sum of the angles must be 180 degrees so:
a + a + d + a + 2d = 180
3a + 3d = 180
dividing by 3
a + d = 60
since a + d = 60 is Y and that this was stated in the question, it follows that they do follow an arithmetic progression given X < Y < Z