HMMT 2025 U12

Holden has a collection of polygons. He writes down a list containing the measure of each interior angle of each of his polygons. He writes down the list $30^{\circ}$ , $50^{\circ}$ , $60^{\circ}$ , $70^{\circ}$ , $90^{\circ}$ , $100^{\circ}$ , $120^{\circ}$ , $160^{\circ}$ , and $x^{\circ}$ , in some order. Compute $x$ .