Question

If four angles of a quadrilateral are as 2:5:6:7, then find the angles of quadrilateral.

Answer 1

Step-by-step explanation:

let the first angle be 2x

the second angle be 5x

the third angle be 6x

the fourth angle be 7x

we know that

the sum of all angles of quadrilateral is 360.

2x+5x+6x+7x=360

20x =360

x = 18

first angles is 2×18 = 36

second angle is 5×18 = 90

third angle is 6×18 = 108

fourth angle is 7×18 = 126

Answer 2

GivEn:

• Four angles of a quadrilateral are in ratio 2:5:6:7

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To find:

• Measure of angles of quadrilateral.

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SoluTion:

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Let the angles of quadrilateral be 2x, 5x, 6x and 7x.

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As we know that,

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Sum of angles of a quadrilateral is 360°

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$:\implies\sf \angle A + \angle B + \angle C + \angle D = 360^\circ$

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$:\implies\sf 2x + 5x + 6x + 7x = 360^\circ$

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$:\implies\sf 20x = 360^\circ$

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$:\implies\sf x = \cancel{ \dfrac{360^\circ}{20}}$

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$:\implies{\underline{\boxed{\sf{\pink{x = 18^\circ}}}}}\;\bigstar$

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★ Now, Put value of x to find the measure of all angles.

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• $\sf \angle A\; (2x) = 2 \times 18 = 36^\circ$

• $\sf \angle B \;(5x) = 5 \times 18 = 90^\circ$

• $\sf \angle C\; (6x) = 6 \times 18 = 108^\circ$

• $\sf \angle D\; (7x) = 7 \times 18 = 126^\circ$

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$\therefore\sf \;\underline{Hence,\;angles\;are\;36^\circ,\;90^\circ,\;108^\circ,\;126^\circ.}$