Question

The sum of measures of a triangle is 180, quadrilateral is 360, pentagon is 540 and so on. Assuming this pattern find the sum of the measures of angles of dodecagon(12 sided polygon) . Only write final number as answer​

Answer 1

No. of sides {3,4,5,.........................} each term rising by 1. Note a dodecagon, a 12 sided polygon will be 10th term.

sum of interior angles {180∘,360∘,540∘,........} each term rising by 180∘ an arithmetic sequence, with first term as 180∘

as nth term of arithmetic sequence, whose first term is a1 and common difference is d is an=a1+(n−1)d.

Hence, 10th term of the sequence representing sum of interior angles of a dodecagon is 180∘+(10−1)×180∘=1800.

Note: Sum of interior angles of a polygon with n sides is 180∘×(n−2).