Question

The ratio between the angles of a quadrilateral is 3:4:5:8 . find angles of the quadrilateral?​

Answer 1

Given: The ratio between the angles of a quadrilateral is 3:4:5:8.

❒ Let the angles of the Quadrilateral be 3x, 4x, 5x and 8x.

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

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• Sum of all angles of Quadrilateral is 360°.

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Therefore,

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$:\implies\sf 3x + 4x + 5x + 8x = 360^{\circ}\\\\\\:\implies\sf 20x = 360^{\circ} \\\\\\:\implies\sf x = \cancel\dfrac{360^{\circ}}{20}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 18^{\circ}}}}}}\:\bigstar$

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❒ Hence, angles of the Quadrilateral are:

• 3x = 3(18) = 54°
• 4x = 4(18) = 72°
• 5x = 5(18) = 90°
• 8x = 8(18) = 144°

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$\therefore\:{\underline{\sf{Hence, \: required\: angles \: are \: \bf{54^{\circ}, \: 72^{\circ}, \: 90^{\circ},\: 144^{\circ}\:}.}}}$⠀⠀⠀⠀⠀

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$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: Verification\: :}}}}}\mid}$

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$:\implies\sf 54^{\circ} + 72^{\circ} + 90^{\circ} + 144^{\circ} = 360^{\circ} \\\\\\:\implies\sf 126^{\circ} + 234^{\circ} = 360^{\circ} \\\\\\:\implies\sf 360^{\circ} = 360^{\circ}$

Answer 2

Answer:

The ratio between the angles of quadrilateral is 3:4:5:8

Let, the angles be 3x , 4x , 5x and 8x.

Since, the sum of angles of quadrilateral is 360°.

Therefore,

3x+4x+5x+8x = 360°

20x = 360°

x = (360/20)°

x = 18°

3x = 3*18° = 54°

4x = 4*18° = 72°

5x = 5*18° = 90°

8x = 8*18° = 144°

Hence, four angles of quadrilateral are 54°, 72°, 90° and 144°.