SOLUTION:  

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Question 1001679:  
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
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The angles of a pentagon are in a ratio of  7:6:5:5:4.  Find the measures of each angle.
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This phrase  "The angles of a pentagon are in a ratio of 7:6:5:5:4"  means that there is a common measure,  x,  of all of these angles,  such that
the 1-st angle is 7 times of this measure,  7x,
the 2-nd angle is 6 times of this measure,  6x,
the 3-rd angle is 5 times of this measure,  5x,
the 4-th angle is 5 times of this measure,  5x,   and
the 5-th angle is 4 times of this measure,  4x.

The sum of internal angles of a pentagon is  180°*(5-2) = 540°,
so you have an equation to find this common measure:

7x + 6x + 5x + 5x + 4x = 540,     or

27x = 540.

Hence,   x = = 20°.

Now you can determine the measure of each angle.

1-st angle is 7*20° = 140°,
2-nd angle is 6*20° = 120°,

and so on . . .



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