Question

The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the
quadrilateral.​

Answer 1

Question:-

The angles of a quadrilateral are in the ratio 3:5:9:13. Find all the angles of the

quadrilateral.

Solution:-

Let us assume that the angles are 3a,5a,9a and 13a.

We know, that in a quadrilateral sum of all angles is 360°.

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So,

=3a+5a+9a+13a=360°

=30a=360°

=a=12°

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So, the angles are,

>3a=3(12°)=36°;

>5a=5(12°)=60°;

>9a=9(12°)=108°;

>13a=13(12°)=196°

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So, thus the angles are 36°,60°,108° and 196°.

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Answer 2

AnswEr :

• The all angles of a quadrilateral is 36°, 60°, 108°, and 156° respectively.

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Explanation :

We are given with the angles of a quadrilateral but we have been given in the ratio, that is,

• 3 : 5 : 9 : 13.

We have to find out the all angles of a quadrilateral$.$

⠀____________________________

Now,

Let us assume that, the angles of a quadrilateral is 3x, 5x, 9x and 13x.

As we are given with the ratio of angles of a quadrilateral.

As we know that

The sum of all angles of a quadilateral is 360°. This statement is known as 'angle sum property of quadrilateral'.

⇒ 3x + 5x + 9x + 13x = 360

⇒ 8x + 9x + 13x = 360

⇒ 17x + 13x = 360

⇒ 30x = 360

⇒ x = 360/30

⇒ x = 36/3

⇒ x = 12

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Therefore,

The all angles of a quadrilateral will be,

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• 3x = 3 × 12 = 36°.

• 5x = 5 × 12 = 60°.

• 9x = 9 × 12 = 108°.

• 13x = 13 × 12 = 156°.

Hence, the all angles of a quadrilateral is 36°, 60°, 108°, and 156° respectively.