Question

Prove that ∆ ABD ≅ ∆CBD. Find the values of x and y, if ∠ = 35°, ∠ = (3 + 5)°, ∠ = ( − 3)°, ∠ = 25°.

Answer 1

Answer:

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°

Hope it will help you..