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