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Question

Find the number of sides of a regular polygon when each of its angles has a measures of (i) 160 (ii) 135 (iii) 175 (iv) 162 (v) 150


Solution

In a n-sided regular polygon, each angle = 2n4n right angles or [2n4n×90]
(i) When each interior angle = 160
Let number of sides of regular polygon=n 
2n4n×90=1602n4n=16090=169
By cross multiplication:
18n36=16n18n16n=362n=36n=362=18
Regular polygon is of 18 sided.  
(ii) Each interior angle = 135
Let number of sides of regular polygon = n
2n4n×90=1352n4n=13590=32
By cross multiplication:
4n8=3n4n3n=8n=8
The regular polygon has 8 sides.
(iii) Each interior angle = 175
Let number of sides of regular polygon = n 
2n4n×90=1752n4n=17590=3518
By cross multiplication:
36n-72=35n
36n35n=72n=72
Regular polygon is of 72 sides.
(iv) Each interior angle = 162
Let number of sides of regular polygon=n 
2n4n×90=162
2n4n=16290=95
By cross multiplication:
10n-20=9n
10n9n=20n=20
Regular polygon is 20sides.
(v) Each interior angle = 150
Let number of sides of regular polygon = n
2n4n×90=1502n4n=15090=53
By cross multiplication,
6n12=5n6n5n=12n=12
The regular polygon of 12 sides. 
 


Mathematics
RD Sharma
Standard VIII

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