Question
Download Solution PDFThe ratio of number of sides of two regular polygons is 4 : 5 and the ratio of their internal angles are 15 : 16. The number of sides of the polygons is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The sides of the two polygons are in the ratio 4 : 5 and the ratio of their internal angles is 15 : 16
Formula used:
Internal angle of a polygon = (n - 2)/n × 180°
Where n = number of sides of the polygon
Calculation:
Let the number of sides of the two polygons be 4x and 5x
According to the formula,
⇒ {(4x - 2)/4x × 180°}/{(5x - 2)/5x × 180°} = 15/16
⇒ (4x - 2)/(5x - 2) × 5/4 = 15/16
⇒ (4x - 2)/(5x - 2) = 3/4
⇒ 16x - 8 = 15x - 6
⇒ x = 8 - 6 = 2
So, the number of sides of the two polygons is 8 and 10.
Last updated on May 28, 2025
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