Question

How many sides would there be in a convex polygon if the sum of all but one of its interior angles is $1070^{\circ}$

Answer 1

Convex Polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.

Lets simplify the given problem,

If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

1070 =[n - 2] x 180, where n = number of sides

$1070 =180n - 360180n =1070+360180n =1430n = 1430 / 180$

n = 7.94 number of sides. Since this is not a whole number, will simply round it up to 8.

Hence the number of sides is 8

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Answer 2

As Convex polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The