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100 Gold Cotton Filled Jewelry Gift Boxes 3 ¼ x 2 ¼ x 1 US $39.90
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Geometry Question!! Help!!?
21.
The jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked. Show Your Work.
http://schools.connectionsacademy.com/content/media/219403-542009-11850-PM-1283664780.jpg
Thanks!!
Since the box is a regular pentagon , the segments of the upper side of the rectangle are equal , the two upper triangles are congruent , etc .. ( let's consider this demonstrated ) ;
Let y = interior angle of the pentagon ;
You know that every angle of a regular "n" sided polygon measures :
θ = 180 (n-2) / n
In case of the pentagon is y = 180 * 3 / 5 = 108
y and the two x are on a straight line , ie
y + 2x = 180 ==> 2x = 180 -108 = 72 ==> x= 36
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