The sides of a pentagon are produced in order and the exterior angles so obtained measure 2x + 20,o, x – 10o, 3x + 30o, 4x – 15o and 5x -10o find the measure of each exterior angle.
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CBSE
Mathematics
Grade 9
Sum of the Measures of the Exterior...
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The sides of a pentagon are produced in order and the exterior angle so obtained are the measures of x degree, 2x degree, (3x + 10) degree, (4x + 5) degree and 5x degree respectively. Find the value of x and the measure of each exterior angle of the polygon.
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Hint: We know that pentagon is a polygon with 5 sides. And for any polygon the sum of exterior angles is 360 degree. Hence we have x + 2x + 3x + 10 + 4x + 5 + 5x = 360.
Complete step by step answer:
Now we are given that the sides of a pentagon are produced in order and the exterior angle so obtained are the measures of x degree, 2x degree, (3x + 10) degree, (4x + 5) degree and 5x degree respectively.
We know that pentagon is nothing but a 5 polygon with 5 sides and for any n sided polygon we have the sum of exterior angles is 360 degree.
Hence we can say that.
x + 2x + 3x + 10 + 4x + 5 + 5x = 360.
Now rearranging the terms we get.
x + 2x + 3x + 4x + 5x + 10 + 5 = 360.
Now let us take x common
(1 + 2 + 3 + 4 + 5)x + 15 = 360
15x + 15 = 360.
Now taking 15 to RHS we get
15x = 360 – 15 = 345.
Hence we have 15x = 345.
Now dividing by 15 on both sides we get
$x=\dfrac{345}{15}=23$
Hence x = 23 degrees.
Now let us substitute x in each angle to find all exterior angles
x degree = 23 degree.
2x degree = 2 × 23 = 46 degree.
(3x + 10) degree = 3 × 23 + 10 = 69 + 10 = 79 degree.
(4x + 5) degree = 4 × 23 + 5 = 92 + 5 = 97 degree.
5x degree = 5 × 23 = 115 degree
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