Question

ABCD is a kite.
The diagonals AC and BD intersect at X.
AC = 12 cm, BD = 20 cm and DX:XB = 3:2 .
Calculate angle ABC.

Answer 1

Given :  ABCD is a kite.  The diagonals AC and BD intersect at X.

AC = 12 cm, BD = 20 cm and DX:XB = 3:2 .

To find :  angle ABC.

Solution:

diagonals AC and BD intersect at X

ABCD is a kite.

DX:XB = 3:2 .

=> AX : CX  = 1 : 1  ( as one Diagonal of kite is bisected)

=> AX = CX = AC/2 = 12/2 = 6 cm

BD = 20 cm

DX : XB = 3 : 2

=> DX = (3/5) * 20 = 12 cm

   & BX   = (2/5) * 20 = 8 cm

AX = 6 cm , BX = 8 cm

∠AXB = 90°  

=> AB = √6² + 8² = 10 cm

 Similarly BC = 10 cm

AC = 12 cm

AC² = AB² + BC² - 2AB.BC Cos∠ABC

=> 12² = 10² + 10² - 2*10*10Cos∠ABC

=> 144 = 200 - 200Cos∠ABC

=> Cos∠ABC = -56/200

=> Cos∠ABC = -7/25

=> ∠ABC = 106.26° ≈ 106°

∠ABC = 106.26° ≈ 106°

Learn more:

In the adjoining figure pqrs is a kite. find the values of X and Y ...

https://brainly.in/question/11614150

Construct a kite TEAM in a which TE=EA=4.5cm , TM =AM =5.2cm and

https://brainly.in/question/13795258