Question

154
ABCD is a square. Two arcs are drawn with A and B as centres, and radius equal to the side
of square. If arcs intersects at point E then measure of ZBDE IS
50

Answer 1

Answer:

30°

Step-by-step explanation:

ABCD is a square. Two arcs are drawn with A and B as centres, and radius equal to the side

of square. If arcs intersects at point E then measure of ∠BDE IS

AE = BE = Radius = Side  of Square = S

in ΔABE

AB  = AE = BE  (equilateral triangle)

=> ∠BAE = 60°

∠A = 90°

=> ∠DAE = ∠A  - ∠BAE = 90° - 60° = 30°

in ΔADE

AD = AE  so ∠ADE = ∠AED

=> ∠ADE + ∠AED + ∠DAE = 180°

=> ∠ADE + ∠ADE + 30° = 180°

=> ∠ADE = 75°

∠ADB = 45°  ( Diagonal angle with side in square)

∠BDE = ∠ADE - ∠ADB

=> ∠BDE =  75° - 45°

=> ∠BDE = 30°