Question 1097500
<br>By drawing all the diagonals from one vertex of a (convex) polygon with n sides, the polygon is divided into (n-2) triangles.  The angle sum in each triangle is 180 degrees; and the sum of the interior angles of the polygon is the sum of all the angles in all the triangles.<br>
(Draw a few figures of polygons with relatively small numbers of sides to see this, if it helps....)<br>
So the sum of the angle measures of a convex polygon with n sides is {{{180(n-2)}}}.<br>
Your angle sum is 3060 degrees; {{{3060/180 = 17}}}; so 17 is (n-2), which means the polygon has 19 sides.