Question

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

Answer 1

LET THE ANGLES BE 3 x , 5 x , 9 x AND 13 x

SUM OF ALL SIDES = 360 degree

SO .. 3 x + 5 x + 9 x + 13 x = 360 degree

30 x = 360

x = 360 / 30

x = 12 degree

so each angles will be

36 , 60 , 108 and 156 .. respectively..

Answer 2

Answer:

$\huge \answer$

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..

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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.