Given : In the figure AB = BC, AD = DC
∠ABD = 50, ∠ADB = y - 7°
∠CBD = x + 5°, ∠CDB = 38°
To find: The value of x and y
In △ABD and △CBD
BD = BD (common)
AB = BC (given)
AD = CD (given)
∴ △ABD ≅ △CBD (SSS axiom)
∴ ∠ABD = ∠CBD
=> 50 = x + 5° => x = 50° - 5 = 45°
and ∠ADB = ∠CDB
⇒ y - 7° = 38° ⇒ y = 38° + 7° = 45°
Hence x = 45°, y = 45°