31. Sum of internal angles of a polygon with 12 sides is (12-2) 180=1800. Measures of angles in the polygon
is in arithrnetie sequence.
a) Find Fum of 6th and 7th term.
b) If the largest angle is 172º find the smallest angle.
c) What is the common difference of this sequence.
d) What are the measure of middle angles.
Answer:
Sum of the interior angles of a polygon of n sides.
=(2n−4)π/2=(n−2)π=(n−2)⋅180o.
Also a=120o,d=5o.
∴2n[2⋅120o+(n−1)5o]=(n−2)⋅180o
Cancel 5 and simplify.
∴n2−25n+144=0
∴(n−9)(n−16)=0.
∴n=9,16.
But when n=16,Tn=a+(16−1)d
=120o+15×5o=195o
This is not possible as interior angle cannot be greater than 180o,
∴n=9 is the correct answer.