Prove theorems about triangles

a) It is possible and it is the only proper value of angle 2

b) Explanation Below

Angle 1 adds to the two other internal angles to get 180

(angle1) + 30 + 42 = 180

angle1 + 72 = 180

angle1 = 180-72

angle1 = 108 degrees

Subtract this from 180 to find the measure of angle 2

angle2 = 180 - angle1

angle2 = 180-108

angle2 = 72

A shortcut is to use the remote interior angle theorem to add up the interior angles 30 and 42 to get 72 as our exterior angle that is not adjacent to any of the interior angles we just added. Hence the "remote" portion.

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18