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Sagot :

If the angles of a convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex] then the smallest angle is 21°.

Given The exterior angles of convex octagon are [tex]2x+6,x+13,2x-1,2x+12,2x-17,3x-4,3x-10,4x.[/tex]

and we have to find the value of smallest angle.

The sum of the  angles of a convex octagon is 360°

so to calculate the smallest angle we need to find out the value of x first and which is calculated by summing up all the exterior angles and put them equal to 360.

(2x+6)+(x+13)+(2x-1)+(2x+12)+(2x-17)+(3x-4)+(3x-10)+4x=360

2x+6+x+13+2x-1+2x+12+2x-17+3x-4+3x-10+4x=360

2x+x+2x+2x+2x+3x+3x+4x+6+13-1+12-17-4-10=360

19x-1=360

19x=360+1

19x=361

x=361/19

x=19

Putting the value of x in all the angles and we will find the following:

2x+6=2*19+6=44

x+13=19+13=32

2x-1=2*19-1=37

2x+12=2*19+12=50

2x-17=2*19-17=21

3x-4=3*19-4=51

3x-10=3*19-10=47

4x=4*19=76

Hence among all the exterior angles the smallest angle is 21°.

Learn more about angles at https://brainly.com/question/25716982

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