Question

Q13 The angles of a quadrilateral are in the ratio 3 : 5:9: 13. Find all the angles of a
quadrilateral.​

Answer 1

↣QUESTION:-

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

↣SOLUTION:-

•Let the angles of the quadrilateral be 3x,5x,9x and 13x respectively.

Now we know that sum of all angles of quadrilateral is 360⁰

Therefore,

3x+5x+9x+13x=360⁰ [by angle sum property of quadrilateral]

30x=360⁰

x=360⁰/30

x=12

Now,

⇢3x =3×12=36⁰

⇢5x =5×12=60⁰

⇢9x =9×12=108⁰

⇢13x=13×12=156⁰

Hence, the required angles of quadrilateral are 36⁰,60⁰.108⁰ and 156⁰ respectively.

↣Verification:-

We know that sum of all angles of quadrilateral is 360⁰

⇢36⁰+60⁰+118⁰+156⁰

⇢360⁰

Hence, verified.