Question

6. In the adjoining figure, ABCD is a kite. If ZBCD = 52°
and ZADB = 42°, find the values of x, y and z.
[Hint. Join AC.)​

Answer 1

Answer:

In triangle ADB

AB=AD

Angle ABD=Angle ADB=42°=x(base angle)

angle A + angle ABD + angle ADB =180°

y+42°+42°=180°

y+84=180

y=180-84

y=96°

Similarly,In triangle BDC

BC=DC

angle CBD = angle CDB(base angle)=z°

angle C + angle CBD + angle CDB =180°

52+z+z=180°

2z=180-52

2z=128

z=128/2

z=64°

Answer 2

Answer:

AD=AB, then, their base angle be same

so that, Angle Abc=x=52°

In triangle CBD,

CD=CB, so that their base angle also be same

Angle CBD +Angle BCD+ Angle CDB

z°+52°+z=180° Angle sum property of triangle

2z=128

then, simplify it

then, z=64

Angle BAD+Angle BDA+Angle DAB

42°+x°+y=180° Angle sum property of triangle

42°+42°+y=180°

84°+y=180°

y=180°-84°

y=96°