The interior angles of a quadrilateral form an arithmetic sequence. If the measure of the largest angle is 129, what is the measure of the second largest angle, in degrees?
We have that
a1 + (3)d = 129 → a1 = 129 - 3d (1)
Where a1 is the first term and d is the common difference
And since the sum of the four angles of a quadrilateral = 360°
a1 + (a1 + d) + (a1 + 2d) + 129 = 360 (2)
Subbing (1) into (2).....we have
129 - 3d + ( 129 - 3d + d) + ( 129 - 3d + 2d ) + 129 = 360 simplify
516 - 6d = 360 subtract 516 from both sides
-6d = -156 divide both sides by -6
d = 26
And ... a1 = 129 - 3(26) = 51°
So.....the second largest angle is 51 + 2*26 = 51 + 52 = 103°