+0  
 
0
57
1
avatar

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
Sort: 

1+0 Answers

 #1
avatar+78577 
+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°

 

 

 

cool cool cool 

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

2 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details