Question

The angles of a quadrilateral are in the ratio 3:5:7:9. Measure the largest angke
angle of quadrilateral -
5 degree
75 degree
105 degree
135 degree​

Answer 1

Answer:

HERE IS UR ANSWER :

Let the ratios of angles of quadrilateral be

• 3x
• 5x
• 7x
• 9x

sum of the angles = 360°

of quadrilateral

3x + 5x+ 7x+ 9x. = 360°

24x. = 360°

x. = 360°/24

x. = 15°

then the angles of quadrilateral will be

3x=3(15)=45°

5x=5(15)=75°

7x=7(15) =105°

9x=9(15)= 135°

hence

the biggest angle of quadrilateral is

135°

..

..

##PHENOMENAL

Answer 2

Solution :

The angles of a quadrilateral are in the ratio 3:5:7:9 & let we suppose the ratio be r;

∠A  = 3r , ∠B = 5r , ∠C = 7r & ∠D = 9r

A/q

As we know that sum of all angles of quadrilateral be 360° then;

$\longrightarrow\sf{\angle A + \angle B + \angle C + \angle D = 360\degree}\\\\\longrightarrow\sf{3r + 5r + 7r + 9r = 360\degree}\\\\\longrightarrow\sf{24r = 360\degree}\\\\\longrightarrow\sf{r=\cancel{360\degree/24}}\\\\\longrightarrow\bf{r=15\degree}$

Thus;

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

∴ The largest angle of a quadrilateral will be 135° .