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?
The smallest and largest angle will sum up to 180.
That means that 180 - 126 = 54 is the small angle.
54 __ __ 126
Can you figure out the blanks?
=^._.^=
Let the smallest angle = a
Let the common difference = d
So
a + 3d = 126 ⇒ a = 126 - 3d ( 1)
And....the sum of the angle measures = 360
a + (a + d) + (a + 2d) + 126 = 360 (2)
Sub (1) into (2)
126 - 3d + 126 - 2d + 126 - d + 126 = 360
504 - 6d = 360
504 - 360 = 6d
144 = 6d
d = 144 / 6 = 24
The second largest angle = 126 - 24 = 102°