Question

quest
que
027. Four angles of a quadrilateral are in the ratio 3:5:7:9. Find all the angles
of a quadrilateral
number of edges in this​

Answer 1

Step-by-step explanation:

sum of all angles of a quadrilateral is 360

so

3x+5x+7x+9x=360

24x=360

x=360/24=15

3x=45

5x=75

7x=105

9x=135

Answer 2

Question :

• Four angles of a quadrilateral are in the ratio 3:5:7:9. Find all the angles of a quadrilateral.

Given :

• Four angles of a Quadrilateral are in the ratio 3:5:7:9 .

To Find :

• All angles of the Quadrilateral

Solution :

✰ As we know that, Angle Sum Property of Quadrilateral states that sum of all the angles of a Quadrilateral equals to 360° which means 1st angle + 2nd angle + 3rd angle + 4rd angle = 360°.

⠀

⟶ Let 1st angle be 3x

⟶ Let 2nd angle be 5x

⟶ Let 3rd angle be 7x

⟶ Let 4th angle be 9x

⠀

According to the Question :

⟹ ∠1 + ∠2 + ∠3 + ∠4 = 360°

⟹ 3x + 5x + 7x + 9x = 360°

⟹ 8x + 16x = 360°

⟹ 24x = 360°

⟹ x = 360 / 24

⟹ x = 15

________________

Therefore :

• 1st angle = 3x = 3 × 15 = 45°
• 2nd angle = 5x = 5 × 15 = 75°
• 3rd angle = 7x = 7 × 15 = 105°
• 4th angle = 9x = 9 × 15 = 135°

________________