Question

The angles of a quadrilateral are in the ratio 3:5:7:9 find the measure of each of the angels ​

Answer 1

$\huge{\boxed{\mathbb{\blue{ANSWER:-}}}}$

Let the ratio of the angles of quadrilateral be x. So the angles will be 3x, 5x, 7x, 9x.

We know that, the sum of all angles of a quadrilateral is always 360°

Given:-

Angles:- 3x, 5x, 7x, 9x

Sum of all angles of a quadrilateral:- 360°

Solution:-

Sum of all angles of the Quadrilateral= 360°

So,

$\tt{3x+5x+7x+9x=360^{\circ}}$

$\longrightarrow\tt{24x=360^{\circ}}$

$\longrightarrow\tt{x={\dfrac{\cancel{360^{\circ}}}{\cancel{24}}}}$

$\longrightarrow{\boxed{\tt{x=15^{\circ}}}}$

So ,

Measure of 1st angle:-

3x=3(15°)=45°

Measure of 2nd angle:-

5x=5(15°)=75°

Measure of 3rd Angle:-

7x=7(15°)=105°

Measure of 4th angle

9x=9(15)=135°

Additional Information:-

$\tt{45^{\circ}+75^{\circ}+105^{\circ}+135^{\circ}=360^{\circ}}$

$\tt{Sum\:of\:all\:angles\:of\:a\:}$ $\tt{quadrilateral\:is\: always \: 360^{\circ}.}$

Hope it helps!

Answer 2

Answer :-

Put x in the ratio

As we know that sum of all angles of a quadrilateral is 360°.

According to question :-

3x + 5x + 7x + 9x = 360°

→ 24x = 360°

→ x = 360°/24

→ x = 15°

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