Question

the angle of quadrilateral are in the ratio 1 ratio 2 ratio 3 ratio 4 what is the measure of your angle of spectraly​

Answer 1

Corrected Question: The angles of a quadrilateral are in the ratio 1:2:3:4. What is the measure of all angles.

Given:

• The angles of Quadrilateral are in the ratio of 1:2:3:4.

To find:

• Measure of all angles.

Solution: Let the measure of all angles of Quadrilateral be x, 2x, 3x and 4x.

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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• Sum of all angles of the Quadrilateral is 360°.

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Therefore,

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$:\implies\sf x + 2x + 3x + 4x = 360 \\\\\\:\implies\sf 10x = 360 \\\\\\:\implies\sf x = \cancel\dfrac{360}{10}\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = 36}}}}}\;\bigstar$

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$\underline{\bf{\bigstar} \:\mathfrak{Angles\;of\; Quadrilateral\:are\: :}}$⠀

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• First angle, x = 36°
• Second angle, 2x = 2(36) = 72°
• Third angle, 3x = 3(36) = 108°
• Fourth angle, 4x = 4(36) = 144°

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$\therefore{\underline{\sf{Hence, \;angles\;of\; Quadrilateral\;are\; \bf{ 36^\circ, 72^\circ, 108^\circ\;and\;144^\circ}.}}}$

Answer 2

${\bf{\red{\underline{\underline{Given\: :-}}}}}$

• The angle of quadrilateral are in the ratio 1 : 2 : 3 : 4

$\\{\bf{\red{\underline{\underline{To\:find \: :-}}}}}$

• Measures of all angles separately.

$\\{\bf{\red{\underline{\underline{Solution\: :-}}}}}$

As we know that sum of all angles of a quadrilateral is equal to 360°.

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• Angles are in the ratio = 1 : 2 : 3 : 4

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Let

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• First angle be x
• Second angle be 2x
• Third angle be 3x
• Fourth angle be 4x

$\\\\\qquad \quad \large{\frak{\underline{\pmb{\purple{According\:to\:the\:question}}}}}$

$\implies\tt x + 2x + 3x + 4x = 360\degree$

• Add in the LHS side

$\\\\\implies\tt 10x = 360\degree$

$\implies\tt x = \dfrac{\cancel{360}\:\:^{36}}{\cancel{10}}$

$\qquad \quad \therefore\tt x = 36\degree$

Substitute the value of x

• First angle = x = 36°
• Second angle = 2x = 72°
• Third angle = 3x = 108°
• Fourth angle = 4x = 144°