The measure of an angle in degrees- grades and radians be D- G and C respectively- then relation between them D-90-G-100-2C- but 1- 180- - - 57-17-44-8- and sum of interior angles of a n-sided regular polygon is 2n-4 -2- On the basis of above information- answer the following questions -The number of sides of two regular polygon are as 5 - 4 and the difference between their angles is -20- then the number of sides in the polygons respectively are -

The correct option is D 10, 8Let the number of side of a polygon be 5x and angle #160; a. amp; for other polygon number of side be 4x and angle #160 ...

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Byju's Answer

Standard VI

Mathematics

Sum of Angles of a Polygon

The measure o...

Question

The measure of an angle in degrees, grades and radians be D, G and C respectively, then relation between them $\frac{D}{90} = \frac{G}{100} = \frac{2 C}{π}$ but $1^{\circ} = {(\frac{180}{π})}^{\circ} ≃ 57^{\circ}, 17^{'}, 44. 8^{''}$ and sum of interior angles of a $n$ -sided regular polygon is $(2 n - 4) \frac{π}{2}$ . On the basis of above information, answer the following questions :The number of sides of two regular polygon are as 5 : 4 and the difference between their angles is $\frac{π}{20},$ then the number of sides in the polygons respectively are -

25, 20

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20, 16

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15, 12

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10, 8

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Solution

The correct option is D 10, 8
Let the number of side of a polygon be 5x and angle $a .$
& for other polygon number of side be 4x and angle $β .$
$a = \frac{(n - 2) π}{n} = \frac{(5 x - 2) π}{5 x} : β = \frac{(4 x - 2) π}{4} a - β = \frac{π}{20} = \frac{π}{x} ((\frac{5 x - 2}{5}) - (\frac{4 x - 2}{4}))$
$\Rightarrow x = 2$
side : $10, 8$

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The correct option is D 10, 8Let the number of side of a polygon be 5x and angle a. & for other polygon number of side be 4x and angle β. a=(n−2)πn=(5x−2)π5x:β=(4x−2)π4a−β=π20=πx((5x−25)−(4x−24))⇒x=2 side : 10,8