Question

8. The angles of a quadrilateral ABCD are in the ratio 3:5:9:13. Find all the angles.​

Answer 1

Given

Angles of a quadrilateral ABCD are given in the ratio 3:5:9:13

To Find

We have to find the angles of a quadrilateral

$\sf\huge {\underline{\underline{{Solution}}}}$

Since,all angles are given in the ratio.So,let the angles be 3x,5x,9x & 13x

Recall property of quadrilateral: All angles of a quadrilateral together makes an angle of 360°.

=> 3x+5x+9x+13x= 360°

=>17x+13x=360

=>30x=360

=>x= 360/30= 12°

x= 12

Now, finding all angles of Quadrilateral

First angle =3x= 36°

second angle= 5x= 5*12=60°

Third angle= 9x=9*12=108°

Fourth angle = 13x= 13*12=156°

Check:

=> 1st angle + 2nd angle +3rd angle +4th angle= 360

=> 36°+60°+108°+156°= 360°

Extra information=>

There are different types of Quadrilateral:

• Square
• Rectangles
• Trapezium
• Rhombus
• Kite
• Parallelogram

Answer 2

Answer↓

=> 3x+5x+9x+13x= 360°

=>17x+13x=360

=>30x=360

=>x= 360/30= 12°

x= 12

First angle =3x= 36°

second angle= 5x= 5*12=60°

Third angle= 9x=9*12=108°

Fourth angle = 13x= 13*12=156°

=> 1st angle + 2nd angle +3rd angle +4th angle= 360

=> 36°+60°+108°+156°= 360°