Question

The interior angles of a polygon are in the ratio 5:6:4:5:7 ,find each angle of the polygon​

Answer 1

★ Answer -

• The angles of the polygon are 80°, 100°, 120°, 100° and 140°.

★ To find -

• The angles of the polygon.

★ Step-by-step explanation -

The interior angles of the polygon are in the ratio 5 : 6 : 4 : 5 : 7.

So let -

• The interior angles of the polygon be 5x, 6x, 4x, 5x and 7x.

We know that -

$\bigstar \: \underline{ \boxed{ \sf Sum_{(angles \: of \: an \: n-sided \: polygon)} = (n - 2) \times 180^{\circ}}}$

Here -

• The number of sides (n) = 5.

Therefore, sum of all the angles of the polygon is -

$\bf \hookrightarrow (n - 2) \times 180^{ \circ}$

$\hookrightarrow \bf (5 - 2) \times 180^{ \circ}$

$\hookrightarrow \bf 3 \times {180}^{ \circ}$

$\hookrightarrow \bf {540}^{ \circ}$

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Now -

$\mapsto\sf5x + 6x + 4x + 5x + 7x = 540$

$\sf \mapsto 27x = 540$

$\mapsto \sf x = \cancel{\dfrac{540}{27} }$

$\mapsto \sf x = {20}^{ \circ}$

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Hence, the angles of the polygon are -

$\implies \tt 4x = 4 \times 20 = {80}^{ \circ}$

$\implies \tt 5x = 5 \times 20 = {100}^{ \circ}$

$\implies \tt 6x = 6 \times 20 = {120}^{ \circ}$

$\implies \tt 5x = 5 \times 20 = {100}^{ \circ}$

$\implies \tt 7x = 7 \times 20 = {140}^{ \circ}$

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Answer 2

Solution :-

given that, the interior angles of a polygon are in the ratio 5:6:4:5:7 .

So, let these angles are 5x, 6x, 4x, 5x and 7x respectively .

we know that,

• sum of interior angles of a polygon with n sides = (n - 2) * 180° .

and given polygon have 5 sides .

then,

→ 5x + 6x + 4x + 5x + 7x = (5 - 2) * 180°

→ 27x = 3 * 180°

→ 27x = 540°

→ x = 20°

therefore,

→ First angle = 5x = 5 * 20 = 100°

→ Second angle = 6x = 6 * 20 = 120°

→ Third angle = 4x = 4 * 20 = 80°

→ Fourth angle = 5x = 5 * 20 = 100°

→ Fifth angle = 7x = 7 * 20 = 140°

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