Question

The interior angles of a regular hexagon are congruent.Why are any pair of opposite sides parallel?

Answer 1

A pair of the opposite sides of a regular hexagon has equal length,

What is a regular hexagon?

A regular hexagon is defined as a closed shape consisting of six equal sides and six equal angles. The sum of the measure of  interior angles of a regular hexagon is 720 degrees.

The total of the interior angles is 180°(n -2), where n is the number of sides of the convex polygon. Thus for a regular polygon of n sides, the interior angles are each.

(180°)(n -2)/n = 180° -(360°/n)

Let us assume the each angle of the hexagon = m

m + m + m + m + m  + m = 720°

or, 6 m = 720°

or, m = 720° / 6 = 120°

Hence Each interior angle of the Regular Hexagon is 120°

A pair of the opposite sides of a regular hexagon has equal length,

Learn more about the regular hexagon here;

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