Question

Angles of quadrilateral are in AP.the ratio of product of first and fourth term to second and third term is 9:10 then find all angles of quadrilateral

Answer 1

Answer:

60,80,100,120

Step-by-step explanation:

let the common diff be 2d

and first angle be A-3d

so second is A-d

third is A+d

fourth be A+3d

we are given that (A-3d)(A+3d)/(A-d)(A+d)=9/10

(A^2-9d^2)/(A^2-d^2)=9/10

9(A^2-d^2)=10(A^2-9d^2)

9A^2-9d^2=10A^2-90d^2

81d^2=A^2

A=9d-----------1 eqn

also sum of angles of quad is 360 degree

(A-3d)+(A-d)+(A+d)+(A+3d)=360

4A=360

A=90

Putting value uf A in eqn 1

90=9d

d=10

so angles are 90-30,90-10,90+10,90+30

=60,80,100,120