Question

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



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Answer 1

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°

Answer 2

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,

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

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

• Sum of the angle of the quadrilateral = 360°

⠀⠀

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

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