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Class 11
Mathematics
Sequence and Series
the difference between any two consecutive interio...

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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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.

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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.

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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.