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

Answers (1)

Consider a triangle ABC which has all sides equal.

We know that angles opposite to equal sides are equal.

Thus we can write :                    \angle A\ =\ \angle B\ =\ \angle C

Also, the sum of the interior angles of a triangle is 180 ^{\circ}.

Hence,                                        \angle A\ +\ \angle B\ +\ \angle C\ =\ 180^{\circ}

or                                                                                3\angle A\ =\ 180^{\circ}

or                                                                                   \angle A\ =\ 60^{\circ}

So, all the angles of the equilateral triangle are equal (60^{\circ}).

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