Question

In the given figure, AB = DB and AC = DC. Find the values of x and y.

Answer 1

In ΔABC and ΔDBC
AB = DB                 ....[given]
AC = DC                 ....[given]
BC = BC                  ....[common]
∴ By Side-Side-Side criterion of congruence,
ΔABC ≅ ΔDBC
∴ ∠ACB =∠DBC    ....[c.p.c.t]
⇒ y + 15° = 63°
⇒ y = 63° - 15°
⇒ y = 48°
Now, ∠ABC = ∠DBC  ....[c.p.c.t]
⇒ 29° = 2x - 4°
⇒ 2x = 29° + 4°
⇒ 2x = 33°
⇒ x = `(33°)/(2)`
⇒ x = 16.5°
Hence, x = 16.5° and y = 48°.