Question 1042358
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<pre>
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.

&#916;ABC is isosceles because AB&#8773;AC, &#8736;B&#8773;&#8736;ACB because they are base angles 
of isosceles &#916;ABC.  &#8736;ACB is acute because the base angles of an isosceles
triangle are always acute. 

&#8736;ACD is obtuse because it is supplementary to acute &#8736;ACB.
&#8736;ACD is the largest angle in &#916;ACD because it is obtuse.
AD is the longest side of &#916;ACD because it is opposite
the largest &#8736;ACD.  AD is longer than AC, because AD is the 
longest side of &#916;ACD.  m(AD) > m(AB), because AB and AC have 
the same measure. m&#8736;B > m&#8736;D because in &#916;ABD, &#8736;B is opposite 
a longer side (AD) than the side &#8736;D is opposite (AB). 
</pre>
2. Prove that there is no regular polygon with an interior angle 
whose measure is 145°.
<pre>
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

{{{(n-2)*"180°"/n}}}.

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 

{{{(n-2)*"180°"/n}}}{{{""=""}}}{{{"145°"}}}, where n is an integer.

Multiply both sides by n

{{{(n-2)*"180°"}}}{{{""=""}}}{{{"145°"n}}}

{{{"180°n"-"360°"}}}{{{""=""}}}{{{"145°"n}}}

Subtract 145°n from both sides

{{{"35°"n-"360°"}}}{{{""=""}}}{{{0}}}

Add 360° to both sides

{{{"35°"n}}}{{{""=""}}}{{{"360°"}}}

Divide both sides by 35°

{{{n}}}{{{""=""}}}{{{360/35}}}

{{{n}}}{{{""=""}}}{{{72/7}}}{{{""=""}}}{{{10&2/7}}}

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</pre>