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