Question

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

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.
Therefore, In fig., ABCD is a square and Δ BEC is an equilateral triangle.

(i) ∠ABE = ∠ABC + ∠CBE

= 90° + 60° = 150°

(ii) But in Δ ABE

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

⇒ 150° + ∠BAE + ∠BAE = 180° .............(∵ AB = BE)

⇒ 150° + 2 ∠BAE = 180°

⇒ 2 ∠BAE = 180°− 150° = 30°

∴ ∠BAE =`(30°)/2=15°`