The interior angles of a quadrilateral form an arithmetic sequence. If the measure of the largest angle is 126 degrees, what is the measure of the second largest angle, in degrees?
+23245 The four angles are a, a + d, a + 2d, a + 3d
---> (a) + (a + d) + (a + 2d) + (a + 3d) = 180
---> 4a + 6d = 360
---> 2a + 3d = 180
Also: a + 3d = 126 ---> 3d = 126 - a
Combining: 2a + 3d = 180 and 3d = 126 - a ---> 2a + (126 - a) = 180
a + 126 = 180
a = 54
The angles are: 54, 78, 102, and 126.
