SOLUTION: I really need help with 2 proofs i would love if someone helped me. thanks! {{{drawing(300,150,-.5,10.5,-.5,5, triangle(0,0,5,0,2.5,4.5),triangle(5,0,2.5,4.5,10.0), locate(0,0,

You write your own 2-column proof.  I'll give you an outline
for it with all the reasons to put into your 2-column proof.

You use the facts that 

1. the largest interior angle and side of a triangle
are opposite each other.
2. the middle side interior angle and side of a triangle
are opposite each other.
3. the smallest interior angle and side of a triangle
are opposite each other.

ΔABC is isosceles because AB≅AC, ∠B≅∠ACB because they are base angles 
of isosceles ΔABC.  ∠ACB is acute because the base angles of an isosceles
triangle are always acute. 

∠ACD is obtuse because it is supplementary to acute ∠ACB.
∠ACD is the largest angle in ΔACD because it is obtuse.
AD is the longest side of ΔACD because it is opposite
the largest ∠ACD.  AD is longer than AC, because AD is the 
longest side of ΔACD.  m(AD) > m(AB), because AB and AC have 
the same measure. m∠B > m∠D because in ΔABD, ∠B is opposite 
a longer side (AD) than the side ∠D is opposite (AB). 

The sum of the interior angles of a polygon with n sides is given 
by the formula

Sum of interior angles = (n-2)*180°

A regular polygon of n sides has n congruent interior angles.
So each interior angle of a regular polygon has measure

.

Assume for contradiction that there exists a polygon on n sides
where n is a positive integer with an interior angle with measure 
145°.  Then 

, where n is an integer.

Multiply both sides by n





Subtract 145°n from both sides



Add 360° to both sides



Divide both sides by 35°





That contradicts the assumption that n is a positive integer.  

Therefore there is no regular polygon with an interior angle 
whose measure is 145°.

Edwin