If the angles of a trapezoid form an arithmetic sequence and the smallest angle measures $60^{\circ}$, what is the measure of the largest angle, in degrees?
I know that an arithmetic sequence is a sequence of numbers where each term is obtained by adding a constant amount to the previous term. Let me call this constant amount $d$. Then the four angles of the trapezoid, from smallest to largest, are $60^{\circ}, 60^{\circ} + d, 60^{\circ} + 2d, 60^{\circ} + 3d$. I also know that the sum of the interior angles of any quadrilateral is $360^{\circ}$. So I can write an equation: $60^{\circ} + (60^{\circ} + d) + (60^{\circ} + 2d) + (60^{\circ} + 3d) = 360^{\circ}$. Simplifying, I get $240^{\circ} + 6d = 360^{\circ}$. Subtracting $240^{\circ}$ from both sides, I get $6d = 120^{\circ}$. Dividing both sides by $6$, I get $d = 20^{\circ}$. Now I can plug this value of $d$ into the expression for the largest angle: $60^{\circ} + 3d = 60^{\circ} + 3(20^{\circ}) = 60^{\circ} + 60^{\circ} = 120^{\circ}$. 