Question

A quadrilateral PQRS is such that its fourth angles are in the ratio 1:3:7:9 . Find the measure of its each angle.​

Answer 1

Answer:-

The four angles of a Quadrilateral PQRS are in the ratio 1 : 3 : 7 : 9.

Let the four angles be x , 3x , 7x , 9x.

We know that,

Sum of four angles of a Quadrilateral = 360°

→ x + 3x + 7x + 9x = 360°

→ 20x = 360°

→ x = 360°/20

→ x = 18°

Therefore,

• 1st angle = x = 18°

• 2nd angle = 3x = 3(18) = 54°

• 3rd angle = 7x = 7(18) = 126°

• 4th angle = 9x = 9(18) = 162°.

Additional Information:-

• A closed figure bounded by four line segments is called a Quadrilateral.

• Sum of four angles of a Quadrilateral = 360°.

• There are different types of quadrilaterals based on sides and angles.

• The line segments joining the opposite vertices of a Quadrilateral are called Diagonals.

Answer 2

Given:

• The ratio of angles of a quadrilateral = 1:3:7:9

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Need to Find:

• Measure of each angle =?

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Solution:

let the angles be:

• x
• 3x
• 7x and
• 9x

We know Sum of all angles in a quadrilateral= 360°

So,

x +3x +7x +9x=360°

==> 20x= 360°

==> x= 18

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Now the angles are:

▪x= 18°

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▪3x

= 3×18

=54°

━━━━━━━━━

▪7x

=7×18

=126°

━━━━━━━━━

▪9x

=9× 18

=162°

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The angles are $\red{18 \degree, \:54 \degree, \: 126 \degree, \: 162 \degree}$