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प्रश्न
The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :
(i) measure of each interior angle ;
(ii) measure of each exterior angle and
(iii) number of sides in the polygon.
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उत्तर
Let exterior angle = x°
Interior angle = 5x°
x + 5x = 180°
6x = 180°
x = 30°
Each exterior angle = 30°
Each interior angle = 5 x 30° = 150°
Let no. of sides = n
∵ each exterior angle = `360^circ/"n"`
`30^circ = (360^circ)/"n"`
n = `(360^circ)/30^circ`
n = 12
Hence (i) 150° (ii) 30° (iii) 12
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