<p>Page 918, Practice Test #9, Section 8, Question #10</p>
<p>If all interior angles of the polygon above are congruent, then x =
A. 60
B. 65
C. 72
D. 80
E. 84</p>
<p>The figure is basically a pentagon with a line extending out of the bottom right corner, and the angle made with that line is x.</p>
<p>First you find the total degrees of the figure. The equation to do that is 180x(n-2) . So 180x(5-2), 180x3=540. Then because you know that the figure is congruent, you divide 540 by so you get 540/5=108. Then because the line coming out of the corner makes a straight line, you know that that makes it a 180 degree angle. Then take 180-108=72. Hope this helps.</p>
<p>There are 540 degrees of interior angles in a pentagon. Since all the angles are congruent, each angle must be 108 degrees. If I understand your diagram correctly, x should equal 72 degrees because angle x is supplementary to the interior angle. So, answer C is correct.</p>
<p>Another way to do it is that if you know that all exterior angles of a polygon sum up to 360, you can just do 360/5=72.</p>