Two regular polygons are such that the ratio between their number of…

Question

Two regular polygons are such that the ratio between their number of sides is 1 : 2 and the ratio of measures of their interior angles is 3 : 4. Then the number of sides of each polygon are

Accepted Answer

Option D. 5, 10. Answer & Solution Answer: Option D Solution: Each interior angle of polygon is given by & = ( x - 2 )x × 180 & Sides is a,\,2a & ( a - 2a ) × 180 ( 2a - 22a ) × 180 = 3/4 & ( a - 2 )a × 2a2 ( a - 1 ) = 3/4 & ( a - 2 ) ( a - 1 ) = 3/4 & 4a - 8 = 3a - 3 & a = 5 & So, sides 5,\,10