<PRE><B>Question 1203593</B>
&lt;br&gt;
&quot;obtuse&quot; means the measure of an angle is greater than 90 degrees.  For a polygon to have all angles obtuse, the average of the angle measures must be greater than 90 degrees.&lt;br&gt;
For a triangle, the average angle measure is 180/3 = 60 degrees.&lt;br&gt;
For any quadrilateral, the average angle measure is 360/4 = 90 degrees.&lt;br&gt;
For any polygon with more than 4 sides, the average angle measure is greater than 90 degrees.&lt;br&gt;
Of the answer choices, the hexagon is the only one with more than 4 sides.&lt;br&gt;
ANSWER: hexagon&lt;br&gt;
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The same solution, using formal algebra....&lt;br&gt;
The sum of the measures of the angles of a polygon with n sides is {{{180(n-2)}}}.&lt;br&gt;
The average measure of an angle of a polygon with n sides is {{{(180(n-2))/n}}}.&lt;br&gt;
We need the average measure of the angles to be greater than 90 degrees:&lt;br&gt;
{{{(180(n-2))/n&gt;90}}}
{{{180n-360&gt;90n}}}
{{{90n&gt;360}}}
{{{n&gt;4}}}&lt;br&gt;
For a polygon to have all obtuse angles, the number of sides of the polygon must be greater than 4.&lt;br&gt;
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