Answer:
(a)59
(b)
Step-by-step explanation:
<u>Part A</u>
The nth term of an arithmetic sequence,
Let the first angle of the triangle =a
Let the common difference = d.
Since the measures of the angles are in an arithmetic progression
We have:
a + (a + d) + (a + 2d) = 180
3a+3d=180
a+d=60
Since a or d cannot be equal to zero, the minimum possible values of a and d is 1 and the maximum possible values of a and d is 59.
Therefore, there are 59 non-similar triangles.
<u>Part B</u>
In an arithmetic sequence
Common difference,
Therefore: