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Question
In the given figure, AB = DB and Ac = DC.
If ∠ ABD = 58o,
∠ DBC = (2x - 4)o,
∠ ACB = y + 15o and
∠ DCB = 63o ; find the values of x and y.
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Solution
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°/(4)`
⇒ X = 16.5°
Thus the values of x and y are :
x = 16.5° and y = 48°
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