Question

The four angles of a quadrilateral are in the ratio 3:5:7:9. Find the angles

Answer 1

$<b>Answer :-</b>$

Angle 1 : 45°
Angle 2 : 75°
Angle 3 : 105°
Angle 4 : 135°

$<b>Step-by-step explanation :</b>$

The four angles are in ratio :- 3 : 5 : 7 : 9

Let the angles be x

➡️ 3x : 5x : 7x : 9x

We know that,
The sum of angles of quadrilateral is 360°

A/q

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

24x = 360

360/24 = x

➡️ x = 15


⛬, Angle 1 =3x=3(15) = 45°
⛬, Angle 2=5x=5(15) = 75°
⛬, Angle 3=7x=7(15) = 105°
⛬, Angle 4=9x=9(15) = 135°


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Answer 2

Solutions :-

Given :
The four angles of a quadrilateral are in the ratio 3:5:7:9

Let the four angles of the quadrilateral be 3x, 5x, 7x and 9x respectively.

We know that,
Sum of all angles of quadrilateral = 360°
=> 3x + 5x + 7x + 9x = 360°
=> 24x = 360°
=> x = 360°/24 = 15°


Hence,
First angle = 3x = 3 × 15° = 45°
Second angle = 5x = 5 × 15° = 75°
Third angle = 7x = 7 × 15° = 105°
Fourth angle = 9x = 9 × 15° = 135°

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