The consecutive angles of a particular trapezoid form an arithmetic sequence. If the largest angle measures 120 degrees, what is the measure of the smallest angle?
Let a be the smallest angle
Let n be the difference between two consecutive angles
a+(a+n)+(a+2n)+(a+3n)=360 (1)
a+3n=120 (2)
Substituting, we have: a+(a+n)+(a+2n)+120=360
a+a+n+a+2n=240
(a+a+a)+(n+2n)=240
3a+3n=240
a+n=80 (3)
(3) * 3 = 3a + 3n = 240 (4)
(4) - (2) => 2a = 120
a = 60 degrees
60 degrees