Question 8
Show that the angles of an equilateral triangle are $60^{\circ}$ each

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Solution

$Δ A B C i s e q u i l a t e r a l w h i c h m e a n s t h a t A B = B C = A C . A B = B C \Rightarrow ∠ B = ∠ C (I n t r i a n g l e, a n g l e s o p p o s i t e t o e q u a l s i d e s a r e e q u a l) . . . (1) A B = B C \Rightarrow ∠ A = ∠ C (I n t r i a n g l e, a n g l e s o p p o s i t e t o e q u a l s i d e s a r e e q u a l) . . . (2) F r o m (1) a n d (2), w e c a n s a y t h a t ∠ A = ∠ B = ∠ C . . . (3) A l s o, ∠ A + ∠ B + ∠ C = 180^{\circ} (A n g l e s u m p r o p e r t y o f t r i a n g l e) P u t t i n g (3) i n t h e a b o v e e q u a t i o n, w e g e t ∠ A + ∠ A + ∠ A = 180^{\circ} \Rightarrow 3 ∠ A = 180^{\circ} \Rightarrow ∠ A = \frac{180}{3} = 60^{\circ} . . . (4) F r o m (3) a n d (4), w e c a n s a y t h a t ∠ A = ∠ B = ∠ C = 60^{\circ}$

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