Math, asked by dutikajena, 8 hours ago


The angles of a quadrilateral are in the ratio of 1:2:3-4. Find the measure of each angle.



Answers

Answered by AestheticSoul
29

Required Answer :

  • First angle = 36°
  • Second angle = 72°
  • Third angle = 108°
  • Fourth angle = 144°

Given :

  • Ratio of the angles of a quadrilateral = 1 : 2 : 3 : 4

To find :

  • The measure of each angle

Solution :

Let the angles of quadrilateral be 1x, 2x, 3x and 4x.

  • First angle = 1x
  • Second angle = 2x
  • Third angle = 3x
  • Fourth angle = 4x

Using formula,

  • Sum of interior angles of a quadrilateral = (2n - 4) × 90°

where,

  • n denotes the number of sides of the polygon

A quadrilateral has 4 sides, 4 angles.

⇒ Number of side (n) = 4

⇒ 1x + 2x + 3x + 4x = (2 × 4 - 4) × 90°

⇒ 10x = (8 - 4) × 90°

⇒ 10x = 4 × 90°

⇒ 10x = 360°

⇒ x = 360°/10

⇒ x = 36°

Substituting the value of 'x' in the angles of quadrilateral :

⇒ First angle = 1x

First angle = 36°

⇒ Second angle = 2x

⇒ Second angle = 2(36°)

Second angle = 72°

⇒ Third angle = 3x

⇒ Third angle = 3(36°)

Third angle = 108°

⇒ Fourth angle = 4x

⇒ Fourth angle = 4(36°)

Fourth angle = 144°

Answered by Sitααrα
130

Appropriate Question:

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

To Find

  • the measure of each of THE four angles

Solution:-

Let all the angles of the quadrilateral be

  • 1 = x
  • 2 = 2x
  • 3 = 3x
  • 4 = 4x

As, we all know,

Sum of the angle of a quadilateral is 360°

 \tt⇛⠀x + 2x + 3x + 4x = 360 {}^{\circ}  \\  \\  \\  \tt⇛⠀⠀⠀⠀10x = 360{}^{\circ}  \\  \\  \\ \tt \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  ⇛⠀⠀⠀⠀x =  \frac{360{}^{\circ} }{10}  \\  \\  \\  \tt \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:\:⇛⠀x= 36{}^{\circ}   \\  \\

Hence,

 \circ \:  \:  \:  \:  \tt \:1st  \:  \:  \: angle \:  \:  \:  \:  \:  =  x= 36  {}^{\circ} \:  \:    \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \\  \\  \circ \:  \:  \:  \:  \tt \:2nd  \:  \:  \: angle \:  \:  \:  \:  \:  = 2x=2 \times 36=72 {}^{\circ} \\  \\  \circ \:  \:  \:  \:  \tt \:3rd  \:  \:  \: angle \:  \:  \:  \:  \:  =3 x=3 \times 36=108 {}^{\circ} \\  \\  \circ \:  \:  \:  \:  \tt \:4th  \:  \:  \: angle \:  \:  \:  \:  \:  = 4x=4 \times 36=144 {}^{\circ} \\  \\

________________________________________

V E R I F I C A T I O N:

  • Sum of the angle of the quadrilateral = 360°

⠀⠀

 \tt⇛⠀⠀⠀⠀x + 2x + 3x + 4x = 360 {}^{\circ}  \\  \\  \\  \tt \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: ⇛   \:  \: \:  \:    \: {36}^{ \circ}  +   {72}^{ \circ} +   {108}^{ \circ} +    {144}^{ \circ} =   {360}^{ \circ} \\  \\  \\  \tt \:⇛ \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    {360}^{ \circ} =   {360}^{ \circ} \:  \:  \:  \:  \:  \:  \:  \:  \\  \\  \\

 \\  \quad \quad \quad \quad{ \pmb{  \mathbb {L.H.S = R.H.S}}} \\  \\  \\

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