Question

The angles of quadrilateral are in the ratio 4: 5: 9: 13. Find all the angles of the quadrilateral.

Answer 1

Answer:

Angles are 60º,100º,180º and 156º

Explanation:

Given :

Ratio 4: 5: 9: 13

To Find :

All angles of the quadrilaterals

Solution :

Let the common ratio between the angles be x. Therefore, the angles will be 4x, 5x, 9x, and 13x respectively.

As the sum of all interior angles of a quadrilateral is 360º,

∴ 4x + 5x + 9x + 13x = 360º

18x = 360º

x = 20º

Hence, the angles are

3x = 3 × 20 = 60º

5x = 5 × 20 = 100º

9x = 9 × 20 = 180º

13x = 13 × 12 = 156º

Answer 2

Step-by-step explanation:

Correct Question:-

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

$\bf{\underline{\underline\red{Given:-}}}$

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

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• All the angles of the quadrilateral.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the common ratio of all the angles be x

So that:-

• 1st angle = 3x

• 2nd angle = 5x

• 3rd angle = 9x

• 4th angle = 13x

As we know that

Sum of angles in a quadrilateral is 360°

→ 1st angle + 2nd angle + 3rd angle+ 4th angle = 360°

→ 3x + 5x + 9x + 13x = 360°

→ 30x = 360°

→ $\rm x = \dfrac{360}{30}$

→ x = 12°

1st angle = 3x = 3 × 12 = 36°

2nd angle = 5x = 5 × 12 = 60°

3rd angle = 9x = 9× 12 = 108°

4th angle = 13x = 13 × 12 = 156°

Therefore the angles are 36° , 60° , 108° and 156°