Question

8. Show that the angles of an equilateral triangle
are 60° each.
​

Answer 1

$\huge{\sf\grey{Given:}}$

$\triangle ABC \: be \: an \: equilateral \: triangle.$

AB = BC = AC[All sides of equilateral triangle are equal]

$\huge{\sf\red{To \: prove:}}$

$\underline{\: \underline\bold{{ \sf \pink{∠A = ∠B =∠C = 60°}}}\:}$

$\huge{\sf\orange{Proof:}}$

$AB=AC$

$\implies ∠C = ∠B$

------>Angle opposite to equal sides are equal ( 1 )

$Also, \: AC = BC$

$\implies ∠A = ∠B$

------->Angle opposite to equal sides are equal ( 2 )

$From ( 1 ) , (2)$

$∠A = ∠B = ∠C$

-------------> ( 3 )

$In \: \triangle ABC$

$∠A + ∠B + ∠C = 180°$

$\implies ∠A = ∠A = ∠A = 180° \: \big[(From3)\big]$

$\implies 3∠A = 180°$

$\implies \boxed{∠A = 60° }$

$\therefore \boxed{∠A = ∠B =∠C = 60°}$

$\underline{ \: \underline{ \: \boxed{∠A = ∠B =∠C = 60°} \: } \: }$

Hence proved.

Answer 2

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