Question

The five angles of a pentagon are in the ratio 5:6:7:8:10. Find all the angles.

Answer 1

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ANSWER

The interior angles of a pentagon are in the ratio 4:5:6:7:5. 

Let angles are 4x,5x,6x,7x and 5x.

 

Sum of all angles of a polygon, having n sides = 180o(n−2)=180o(5−2)=540o

Now,

4x+5x+6x+7x+5x=

Answer 2

WKT angle sum property of a Pentagon is 540°

therefore let the above angles be 5x,6x,7x,8x and 10x.

Now let's add them

5x + 6x + 7x + 8x + 10x = 36x

So, 35x = 540°

540°÷36 = x

x = 15°

Hence the angles are

75° ,90°, 105° ,120° and 150°

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