Question

prove that all angles of eqilateral triangle measures 60°​

Answer 1

Answer:

$\sf \huge \underline{note \ \: : }$

$\blue \bull \sf \: all \: the \: angles \: are \: equal \: in \\ \sf \: equilateral \: triangle. \: \: \: \: \: \: \: \:$

$\blue\bull \sf \: all \: the \: sides \: \: are \: equal \: in \\ \sf \: equilateral \: triangle. \: \: \: \: \: \: \: \:$

$\sf \huge \underline{let \: us \: solve}$

$\sf \blue \bull \: let \:the \: unknown \: angle \: be \: (x)$

$\sf \to \: x + x + x = 180(interior \: angle \: of \: triangle)$

$\sf \to \: 3x = 180$

$\sf \to \: x = \frac{180}{3}$

$\red {\sf{{x = 60}}}$

$\sf \huge \underline{hence \: proved \ \: : }$

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Answer 2

Answer:

GIVEN - ABC ia a eqilateral Triangle where

AB =BC=CD

TO PROVE - ANGLE A = ANGLE B= ANGLE C = 60°

PROVE- LET ANGLE A be x

and angle A = angle B =angle C = x

By angle sum property of a triangle

angle A + angle B +angle c = 180

x + x + x = 180

3x = 180

x = 180 /3

x = 60°

then,

ANGLE A = ANGLE B = ANGLE C = 60°

HENCE PROVED