Math, asked by shivasinghmohan629, 4 months ago

question for genius rank​

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Answered by AshMaXSiRa
3

We will use the angle sum property of a quadrilateral to find the measure of all the angles of the quadrilateral.

It is given that the angles of the quadrilateral are in the ratio 3: 5: 9: 13.

Let the four angles be 3x

, 5x

, 9x

, and 13x

respectively.

Now, the angle sum property of a quadrilateral states that the sum of the measures of the four interior angles of a triangle is always 360∘

.

Thus, the sum of the two four angles will be equal to 360∘

.

Therefore, we get

3x+5x+9x+13x=360∘

We will solve this equation to find the value of x

.

Adding the like terms in the equation, we get

⇒30x=360∘

Dividing both sides of the equation by 30, we get

⇒30x30=360∘30⇒x=12∘

We get the value of x

as 12∘

.

Finally, we will substitute the value of x

to find the measures of all the angles of the quadrilateral.

Substituting x=12∘

in 3x

, we get the first angle of the quadrilateral as

3x=3×12∘=36∘

Substituting x=12∘

in 5x

, we get the second angle of the quadrilateral as

5x=5×12∘=60∘

Substituting x=12∘

in 9x

, we get the third angle of the quadrilateral as

9x=9×12∘=108∘

Substituting x=12∘

in 13x

, we get the fourth angle of the quadrilateral as

13x=13×12∘=156∘

The measures of all the angles of the quadrilateral are 36∘, 60∘, 108∘and 156∘

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Answered by mundrakol
1

Step-by-step explanation:

It is a simple question

even a beginner rank can also solve it

Let ratio = 3x,5x,9x,13x

3x+5x+9x+13x= 360

30x = 360

x= 12

1st angle = 36°

2nd angle = 60°

3rd angle = 108°

4th angle = 156°

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