In the given figure, ABCD is a square, BCXYZ is a regular pentagon and ABE is an equilateral triangle. What is the value (in degrees) of ∠EBZ ?

Solution (By Examveda Team)

AB = BC = CD = DA
BC = CX = XY = YZ = BZ
AB = BE = AE
In ΔABE
∠A = ∠B = ∠E = 60°
In Pentagon BCXYZ
Each internal angle of a pentagon = $$\frac{{\left( {n - 2} \right) \times 180}}{n}$$
∠ZBC = $$\frac{{3 \times 180}}{5} \times {108^ \circ }$$
∠EBZ + ∠ABE + ∠ABC + ∠ZBC = 360°
∠EBZ + 60° + 90° + 180° = 360°
∠EBZ = 102°