Question

The angles of a pentagon are in ratio

9:10:12:14:15. What is the sum of measures of
the smallest and largest angles?

Answer 1

216* is the sum of measures of the smallest and largest angles

Answer 2

216°

Explanation:

The ratio of the sum of smallest and largest to the total of all angles is ...

(9 +15)/(9 +10 +12 +14 +15) = 24/60 = 0.4

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The total of all angles in an n-gon is 180°(n -2), so the total of all angles in a pentagon is ...

180°(5 -2) = 540°

Then the sum of smallest and largest angles is ...

0.4(540°) = 216°