Question

In the given figure, AB = DB and Ac = DC.

If ∠ ABD = 58^o,
∠ DBC = (2x - 4)^o,
∠ ACB = y + 15^o and
∠ DCB = 63^o ; find the values of x and y.

Answer 1

Given:
In the figure AB = DB, AC = DC, ∠ABD =  58°,
∠DBC = ( 2x - 4 )°, ∠ACB = ( y +15)° and ∠DCB = 63°
We need to find the values of x and y. 

In ΔABC and ΔDBC
AB = DB              ...[ Given ]
AC= DC               ...[ Given ]
BC= BC                ...[ common ]
∴ By Side-SIde-Side criterion of congruence, we have,
ΔABC ≅ ΔDBC
The corresponding parts of the congruent triangles are congruent.
∴ ∠ABC= DCB       ...[ c. p. c .t ]
⇒ y° + 15° = 63° 
⇒ y° = 63° - 15°  
⇒ y° = 48°  
and ∠ABC =∠DBC  ...[ c.p.c.t ]
But, ∠DBC = ( 2x  - 4)°  
We have ∠ABC + ∠DBC = ∠ABD
⇒ (2x  - 4)° + (2x - 4)°  = 58°  
⇒  4x - 8^°= 58^°
⇒  4x = 58^° + 8^°
⇒  4x = 66^°
⇒  X = ` 66<sup>°</sup>/(4)`
⇒  X = 16.5^°
Thus the values of x and y are :
x = 16.5°  and y = 48^°