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<p>Equal regular pentagons are placed together to form a ring as shown in the diagram, which shows the first three pentagons.</p>
<p>How many more pentagons are needed to complete the ring?</p>
<p style="text-align: center;"><mdo:image alt="circle with chain of 3 pentagons." height="151" src="problem.jpg" title="circle with chain of 3 pentagons." width="145"></mdo:image></p>
<p style="text-align: center;"> </p>
<p>If you liked this problem, <a href="http://nrich.maths.org/public/viewer.php?obj_id=4832&part=index&refpage=monthindex.php">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p></mdoxml>
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<p>Each pentagon has a turn of 36<sup>o</sup> to pack against its
neighbour.</p>
<p>Therefore it will take 10 (x36<sup>o</sup>) turns to complete a
full-turn, i.e. 10 pentagons</p>
<p>Therefore 7 more pentagons are needed.</p>
<p><mdo:image src="solution.gif" alt="chain of 10 pentagons around a circle" title="chain of 10 pentagons around a circle" width="178" height="185"></mdo:image></p>
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Weekly Problem 47 - 2011
Weekly Problem 47 - 2011
Secondary Mapping Document
Angles and polygons