Question

10. Find the smallest and the greatest angle of a pentagon whose angles are in the ratio 6:3:2:5:4.​

Answer 1

Solution :

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The angles of a Pentagon are in the ratio of 6:3:2:5:4. We have to find the smallest and greatest angles.

Let the angles be 6x, 3x , 2x, 5x and 4x respectively.

Sum of all the angles of a Pentagon : (5-2) × 180° = 540°

>> 6x + 3x + 2x + 5x + 4x = 540

>> 20x = 540

>> x=27.

Smallest angle >> 54°

Largest angle >> 162 °

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Answer 2

Answer:

Given :-

Ratio of sides of a Pentagon = 6:3:2:5:4

To Find :-

Smallest and greatest angle

Solution :-

Let the ratio 6y, 3y, 2y, 5y and 4y

$\sf \implies \: 6y + 3y + 2y + 5y + 4y = 540$

$\sf \implies 9y + 11y = 540$

$\sf \implies \: 20y = 540$

$\sf \implies \: y = \dfrac{540}{20}$

$\sf \implies \: y = 27$

Henceforth,

Greatest angle = 6y = 6(27) = 162⁰

Smallest angle = 2y = 2(27) = 54⁰