Question 1003321
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Angles of a pentagon in the ratio 2:3:5:8:12. Find the smallest and the largest {{{highlight(angles)}}}.
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This phrase &nbsp;"Angles of a pentagon in the ratio &nbsp;2:3:5:8:12."&nbsp; means that there is an angle &nbsp;{{{alpha}}}, &nbsp;which is a &nbsp;"<U>common measure</U>" &nbsp;of the five angles in a way that


&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;1-st angle is equal to &nbsp;{{{2alpha}}},

&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;2-nd angle is equal to &nbsp;{{{3alpha}}},

&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;3-rd angle is equal to &nbsp;{{{5alpha}}},

&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;4-th angle is equal to &nbsp;{{{8alpha}}}, and

&nbsp;&nbsp;&nbsp;&nbsp;the &nbsp;5-th angle is equal to &nbsp;{{{12alpha}}}.


Then the sum of these angles is {{{(2 + 3 + 5 + 8 + 12)*alpha}}} = {{{30*alpha}}}.


From the other side, the sum of interior angles of a pentagon is (5-2)*180° = 3*180° = 540°.


Hence, {{{alpha}}} = {{{540/30}}} = 18°.


Now you can easily determine all 5 angles and determine the smallest and the largest. Do it yourself, please.