Question

the angles of a quadilateral are in the ratio 2:4:5:7 .find the angles.

Answer 1

let the angles be 2x,4x,5x,7x

Sum of all angles of a quadrilateral is 180degree

$2x + 4x + 5x + 7x = 180 \\ 18 x = 180 \\ x = \frac{180}{18}$

$\large{\implies{x=10}}$

The angles are :

$2x = 2(10) = 20degree \\ 4x = 4(10) = 40degree \\ 5x = 5(10) = 50degree \\ 7x = 7(10) = 70degree$

Answer 2

Answer:

∠1 = 40°

∠2 = 80°

∠3 = 100°

∠4 = 140°

Explanation:

Let angles of the quadrilateral be ∠1 and ∠2 and ∠3 and ∠4

By Angle sum property of a quadrilateral

∠1+∠2+∠3+∠4=360           ----(1)

and, let ∠1=2x              (given)              ---------(2)

similarily ∠2=4x                                     ---------(3)

similarily ∠3=5x                                     ---------(4)

similarily ∠4=7x                                     ---------(5)

Replacing ∠1,∠2,∠3,∠4 in (1)

⇒2x+4x+5x+7x=360

=18x=360

=x=$\frac{360}{18}$

=x=$\frac{20}{1}$

=x=20 degree                 -------(6)

Putting (6) in (2)

∠1 = 2x = 2×20 = 40 degree

Putting (6) in (3)

∠2 = 4x = 4×20 = 80 degree

Putting (6) in (4)

∠3 = 5x = 5×20 = 100 degree

Putting (6) in (5)

∠4 = 7x = 7×20 = 140