Question

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

Answer 1

$Given \: ratio \: of \: angles \:in\:a \: Pentagon$

$= 6:3:2:5:4$

$Sum \: of \:the \:ratio$

$= 6+3+2+5+4$

$=20$

$20\:parts = 540\degree$

$\boxed { \pink { Sum \:of \:the \: angles \: in \:a \: Pentagon = 540\degree }}$

$\implies 1 \:part = \frac{540}{20}$

$\implies 1\:part = 27 \degree$

$Now, \red{Measure \:of \: smallest \:angle}$

$=2\:parts$

$= 2\times 27$

$\green{= 54\degree}$

$and, \red{Measure \:of \: greatest \:angle}$

$=6\:parts$

$= 6\times 27$

$\green{= 162\degree}$

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Answer 2

Given :

• angle of a pentagon whose angles are in the ratio 6:3:2:5:4

To Find :

• smallest and the greatest angle of a pentagon

Solution :

Let, the multiple of ratio be x

Sum of all angles of pentagon = 540°

⇒ 6x + 3x + 2x + 5x + 4x = 520°

⇒ 20x = 520°

⇒ x = 520°/20

⇒ x = 27°

_____________________

Greatest angle of pentagon = 6x

⇒ Greatest angle of pentagon = 6 × 27°

⇒ Greatest angle of pentagon = 162°

_____________________

Smallest angle of pentagon = 2x

⇒ Smallest angle of pentagon = 2 × 27°

⇒ Smallest angle of pentagon = 54°