+0  
 
0
81
1
avatar

The measures of the interior angles of a convex 9-gon form an arithmetic sequence and, measured in degrees, are all distinct integers. What is the measure of the largest possible angle if the smallest angle is 100 degrees?

 Jul 22, 2022
 #1
avatar+124676 
+1

The  interior  angles sum to   180 (9 -2)  =  1260°

 

So

 

100 + (100 + d) + (100 +2d)  + (100 + 3d)  +(100 + 4d) + (100 + 5d) + (100 + 6d) + (100 + 7d) +

(100 + 8d)  =  1260

 

900 + 36d =  1260

 

36d =  360

 

d =  10

 

Largest angle =     100 + 8 (10) =  180°

 

 

cool cool cool

 Jul 22, 2022

10 Online Users