Concept of Ratio between 2 Quantities Using Line Segments
Question 140T...
Question
Question 140
The ratio between exterior angle and interior angle of a regular polygon is 1 : 5. Find the number of sides of the polygon.
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Solution
Let the exterior angle and interior angle be x and 5x, respectively.
Then, x+5x=180∘
[∵ exterior angle and corresponding interior angle are supplementary] ⇒6x=180∘⇒x=180∘6⇒x=Exteriorangle=30∘ ∴ The number of sides =360∘Exteriorangle =360∘30∘ =12