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?
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sum of angles in pentagon 540°
taking the angles as 9x,10x,12x,14x and 15x
therefore, using angle sum property of pentagon
9x+10x+12x+14x+15x = 540
=> 60x = 540
=> x = 540/60
=> x = 9
now, 9x= 9×9= 81°
10x= 10×9 = 90°
12x = 12×9 =108°
14x = 14×9= 126°
15x = 15×9 = 135°
the angles are- 81° , 90° , 108° , 126° and 135°.
sum of smallest and largest angles
=> 81+ 135
=> 216
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