Question

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

Answer 1

Answer:

The angles of the quadrilateral are

60, 80, 100, 120

Step-by-step explanation:

Let the angles of the quadrilateral be a, a+d, a+2d, a+3d

since sum of the interior angles of the quadrilateral is 360,

a+(a+d)+(a+2d)+(a+3d)=360

4a+6d =360

2a+3d=180...............(1)

Also,

a(a+3d) : (a+d)(a+2d) = 9 : 10

$\frac{a^2+3ad}{a^2+3ad+2d^2}=\frac{9}{10}$

$10a^2+30ad=9a^2+27ad+18d^2$

$a^2+3ad-18d^2=0$

$(a+6d)(a-3d)=0$

a= -6d, 3d

a=-6d is not possible

put a=3d in (1) we get

2(3d)+3d=180

9d=180

d=20

a=3(20)=60

Therefore

The angles of the quadrilateral are

60, 80, 100, 120