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The difference between any two consecutive interior angles of a polygo...

The difference between any two consecuti | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Question:

The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

Answer:

The angles of the polygon will form an A.P. with common difference d as 5° and first term a as 120°.

It is known that the sum of all angles of a polygon with n sides is 180° (n – 2).

$S subscript n equals 180 to the power of 0 open parentheses n minus 2 close parentheses rightwards double arrow n over 2 open square brackets 2 a plus open parentheses n minus 1 close parentheses d close square brackets equals 180 to the power of 0 open parentheses n minus 2 close parentheses rightwards double arrow n over 2 open square brackets 240 to the power of 0 plus open parentheses n minus 1 close parentheses 5 to the power of 0 close square brackets equals 180 open parentheses n minus 2 close parentheses rightwards double arrow n open square brackets 240 plus open parentheses n minus 1 close parentheses 5 close square brackets equals 360 open parentheses n minus 2 close parentheses rightwards double arrow 240 n space plus space 5 n squared space minus 5 n space equals space 360 n space minus 720 rightwards double arrow 5 n squared plus 235 n minus 360 n space plus 720 equals 0 rightwards double arrow 5 n squared space minus 125 n space plus 720 equals 0 rightwards double arrow n squared minus 25 n space plus space 144 space equals space 0 rightwards double arrow n squared minus 16 n minus 9 n plus 144 equals 0 rightwards double arrow n open parentheses n minus 16 close parentheses minus 9 open parentheses n minus 16 close parentheses equals 0 rightwards double arrow open parentheses n minus 9 close parentheses open parentheses n minus 16 close parentheses equals 0 rightwards double arrow n equals 9 space o r space 16$

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Comments

VERISHA COLTON
2019-01-17 20:57:15

They say that the difference between ANY two consecutive angles. So it could be the last and the first one as well but then like Lalit Mohan said the difference is more than 5Â°. Could you please explain?

Simran
2017-09-06 06:28:39

Here difference between 16 and 9 is seven. So rejected the value of n=16. So number of sides of polygon is 9.

LALIT MOHAN SAINI
2015-11-23 13:41:56

Here first and last angles are also consecutive, but difference is more than 5.

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Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 18: The difference between any two consecutive interior angles of a polygon is 5°. If the smallest a....

The difference between any two consecuti | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

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