Respuesta :

alyssa29464
Try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

1070 =[n - 2] x 180 (n = number of sides)
1070 =180n - 360
180n =1070+360
180n =1430
n = 1430 / 180
n = 7.94 number of sides.

Round the number up to 8 since 7.94 isn’t whole.

So, the convex polygon is an octagon with sum of its interior angles:

[8 - 2] x 180 =1080 degrees.
Athenalsun

Answer:

8

Step-by-step explanation:

The sum of the interior angles in any n-sided polygon is 180(n-2) degrees, so the angle measures in a polygon with 7 sides sum to 180(7-2) = 900 degrees, which means that the desired polygon has more than 7 sides. Meanwhile, the angle measures in a polygon with 8 sides sum to 180(8-2) = 1080 degrees. So, it's possible that the polygon has 8 sides, and that the last angle measures 10 degrees

To see that this is the only possibility, note that the angle measures in a polygon with 9 sides sum to 180(9-2) = 1260 degrees. Therefore, if the polygon has more than 8 sides, then the last interior angle must measure at least 1260 - 1070 = 190 degrees. But this is impossible because each interior angle of a convex polygon has measure less than 180.

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