How many sides would there be in a convex polygon if the sum of all but one of its interior angles is 1070 degrees?

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.