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# Help

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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?

Sep 10, 2017
edited by Guest  Sep 10, 2017

### 1+0 Answers

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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°   Sep 10, 2017
edited by CPhill  Sep 10, 2017