SOLUTION: Angles of a pentagon in the ratio 2:3:5:8:12. Find the smallest and the largest anglese

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Question 1003321: Angles of a pentagon in the ratio 2:3:5:8:12. Find the smallest and the largest anglese
Answer by ikleyn(52786) About Me  (Show Source):
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Angles of a pentagon in the ratio 2:3:5:8:12. Find the smallest and the largest highlight%28angles%29.
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This phrase  "Angles of a pentagon in the ratio  2:3:5:8:12."  means that there is an angle  alpha,  which is a  "common measure"  of the five angles in a way that

    the  1-st angle is equal to  2alpha,
    the  2-nd angle is equal to  3alpha,
    the  3-rd angle is equal to  5alpha,
    the  4-th angle is equal to  8alpha, and
    the  5-th angle is equal to  12alpha.

Then the sum of these angles is %282+%2B+3+%2B+5+%2B+8+%2B+12%29%2Aalpha = 30%2Aalpha.

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

Hence, alpha = 540%2F30 = 18°.

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