Question

In the figure, given below, ABCD is a square, and ∆ BEC is an equilateral triangle. Find, the case:∠BAE

Answer 1

We know that the sides of a square are equal and each angle is of 90°

Three sides of an equilateral triangle are equal and each angle is of 60.
In fig.,

∴ ABCD is a square and Δ BEC is an equilateral triangle,

(i) ∠ABE = ∠ABC − ∠CBE

= 90° − 60° = 30°

(ii) In Δ ABE,

∠ABE + ∠AEB + ∠BAE = 180° ...............(Angles of a triangle)

⇒ 30° + ∠BAE + ∠BAE = 180° .............(∵ AB = BE)

⇒ 30° + 2∠BAE = 180°

⇒ 2 ∠BAE = 180°− 30° = 150°

⇒ ∠BAE =`(150°)/2=75°`