SOLUTION: Interior angles of an octagon ABCDEFGH are in A.P.the largest and second an average of 153.find the average of least two.

The nth term of an arithmetic sequence (numbers in A.P.) is

given by the formula:







The largest interior angle is the octagon is 











The second interior angle is the octagon is 











The average of the largest and second interior angles is







We are told this average is 153°



(eq. 1)  



The sum of n terms of an arithmetic sequence (numbers in A.P.) is

given by the formula:







Substituting n=8







(eq. 2)   



The sum of the measurements of the interior angles of an n-sided

polygon is given by the epression 







For an octagon, n=8.



Sum of the interior angles of the octagon is 







Therefore .  Substituting that in (eq. 2)







Dividing both sides by 4



 



or



{eq. 3)   



So we have this system consisting of eqs. 1 and 3



 

 

Solve the first equation of the system for 



(eq. 4)   



Substituting in the second equation of the system























Substituting in (eq. 4)











So the least interior angle of the octagon is the first

term 9°, and the common difference is d=36°



So the second term  = 9° + 36° = 45°.



The average of the least two interior angles is:







Answer: 27°



Edwin