Question

The argles of quadsvilateral are
in the ratio 3:5:9:13 Find all
the angles of the quo docitat eral​

Answer 1

Step-by-step explanation:

We know that sum of angles of quadrilateral = 360⁰

Now acoording to the question 360⁰=3:5:9:13

$so$

$angles = \\ 3x \\ 5x \\ 13x$

$3x + 5x + 9x + 13x = 360 \degree \\ \implies30x = 360 \degree \\ \implies x \: = \cancel \dfrac{360 \degree}{ 30} = 12\\ x = 12 \\ so \\ 12 \times 3 =36\degree \\ 5 \times 12 = 60 \degree \\ 9 \times 12 =108 \degree \\ 13 \times 12 = 156 \degree$

Answer 2

Correct Question :

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

Answer :

The angles are,

• 36°
• 60°
• 108°
• 156°

Step-by-step explanation :

To Find,

• All angles of the quadrilateral

Solution,

Given that,

• The angles are in a ratio of 3 : 5 : 9 : 13

Let us assume the ratio angles as, 3x, 5x, 9x and 13x

As we know that,

Sum of all angles of quadrilateral = 360°,

➟ 3x + 5x + 9x + 13x = 360°

➟ 3x + 5x + 9x + 13x = 360

➟ 8x + 9x + 13x = 360

➟ 17x + 13x = 360

➟ 30x = 360

➟ x = 360 / 30 ..... cancelling zeros from both the numerator and denominator

➟ x = 36 / 3

➟ x = 12

The value of x is 12.

The angles of quadrilateral are,

⋄ 3x

➟ 3 × 12

➟ 36°

⋄ 5x

➟ 5 × 12

➟ 60°

⋄ 9x

➟ 9 × 12

➟ 108°

⋄ 13x

➟ 13 × 12

➟ 156°

The angles of quadrilateral are, 36°, 60°, 108° and 156°.