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?

Guest Sep 10, 2017

edited by
Guest
Sep 10, 2017

#1**+1 **

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°

CPhill
Sep 10, 2017