Question

question for branily star​

Answer 1

Step-by-step explanation:

Given :

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

To find :

All the angles of the quadrilateral.

Solution :

Let the angles of the quadrilateral be:

• 3x
• 5x
• 9x
• 13x

Then we know, in a quadrilateral sum of interior angles is equal to 360°.

That is:

⇒ 3x + 5x + 9x + 13x = 360°

⇒ 30x = 360°

⇒ x = 360°/30

⇒ x = 12°

Hence, the angles are:

⇒ 3x = 36°

⇒ 5x = 60°

⇒ 9x = 108°

⇒ 13x = 156°

Verification :

• 3x + 5x + 9x + 13x = 360°
• 36° + 60° + 108° + 156° = 360°
• 96° + 264° = 360°
• 360° = 360°

∴ L.H.S = R.H.S

...ッ

Answer 2

Question :

The ratio of the angles of quadrilateral is 3 : 5 : 9 : 13. Find all the angles of this quadrilateral.

Solution :

Here, we are given the ratio of the four angles of quadrilateral, i.e. 3 : 5 : 9 : 13 and we need to calculate the four angles. For that we will assume the four angles as any variable, according to the ratio given. Then by using the formula of sum of interior angles of polygon, we will get our required answer.

A quadrilateral has 4 angles, 4 side.

= Number of sides (n) = 4

Sum of interior angles of polygon = (2n - 4) × 90°

where,

• n = number of sides of the polygon

Let,

• The first angle = 3x
• The second angle = 5x
• The third angle = 9x
• The fourth angle = 13x

= 3x + 5x + 9x + 13x = (2(4) - 4) × 90°

= 30x = (8 - 4) × 90°

= 30x = 4 × 90°

= 30x = 360°

= x = 360°/30

= x = 36°/3

= x = 12°

Substituting the value of 'x ' in the angles of quadrilateral :

= The first angle = 3x

= The first angle = 3(12°)

= The first angle = 36°

= The second angle = 5x

= The second angle = 5(12°)

= The second angle = 60°

= The third angle = 9x

= The third angle = 9(12°)

= The third angle = 108°

= The fourth angle = 13x

= The fourth angle = 13(12°)

= The fourth angle = 156°