Question

From the following figure..find the value of x and y.

Answer 1

In ΔABC and ΔEDC , we have

AC = CE ( Given )

∠ACB = ∠ECD ( Vertically Opposite Angles )

∠BAC = ∠DEC ( Given )

∴ ΔABC ≅ ΔEDC

∴ BC = DC (CPCT) ------------------ (i)

∴ AB = ED (CPCT)--------------------(ii)

∴ Putting values in eq. (i)

x = 2y

So, 2x + 4 = 2(2y) + 4

                 = 4y + 4 -----------------(iii)

From eq.(ii) and eq. (iii)

   AB = ED

⇒ 2x + 4 = 3y +8

⇒ 4y + 4 = 3y + 8

⇒4y - 3y = 8 -4

⇒ y = 4

∴ x = 2y = 2×4 = 8

and, y = 4