The sum of the measures of the interior angles of a convex polygon is 1260 deg. Find the no. of sides of the?

Question

polygon. Pls. explain. Is there a formula for this? Thanks!

Answer 1

Use the formula (n-2)*180 =1260 to solve this problem. Start by dividing both sides by 180 to get:(n-2)=7. This means that n=9

Answer 2

Don't let the word induction scare you. The principle can be used here:

triangle, 3 sides, pi deg = (n-2)*pi . 180 deg
rectangle, 4 sides, 2*pi deg= (n-2)*pi, 360 deg
...
octagon, 8 sides, 8*(pi-pi/4)= 6*pi

Thus, for n sides the sum of the interiour angles is (n-2)*pi

so/ 1260/180 = 7 = n-2, thus n = 9 sides.

1260 =