We will work backwards to get the answer. First find each exterior angle of a regular hexagon

A hexagon has 6 sides (n=6) and the formula for each exterior angle of a regular polygon is $latex \displaystyle \frac{{{{{360}}^{o}}}}{n}$

$latex \displaystyle \frac{{{{{360}}^{o}}}}{6}={{60}^{o}}$

Secondly, find the interior angle of the regular *n*-sided polygon.

$latex \displaystyle {{60}^{o}}+{{48}^{o}}={{108}^{o}}$.

Thirdly, find the number of sides of the *n*-sides polygon.

Use the formula that is use to find each interior angle of a regular polygon $latex \displaystyle \frac{{\left( {n-2} \right)\times {{{180}}^{o}}}}{n}$

$latex \displaystyle \frac{{\left( {n-2} \right)\times {{{180}}^{o}}}}{n}={{108}^{o}}$

$latex \displaystyle \left( {n-2} \right)\times {{180}^{o}}={{108}^{o}}n$

$latex \displaystyle {{180}^{o}}n-{{360}^{o}}={{108}^{o}}n$

$latex \displaystyle {{180}^{o}}n-{{108}^{o}}n={{360}^{o}}$

$latex \displaystyle {{72}^{o}}n={{360}^{o}}$

$latex \displaystyle n=\frac{{{{{360}}^{o}}}}{{{{{72}}^{o}}}}$

$latex \displaystyle n=5\ \text{sides}$

You must remember to memorize the formulas for polygons i) Sum of Interior Angles of a Polygon (In your textbook) ii) Each Interior Angle of a Regular Polygon (Formula above) iii) Each Exterior Angle of a Regular Polygon (Formula above). These formulas are **NOT** given in the Exam formula sheet. If you don’t memorize, you will not be able to do these questions.

New Elementary Math (E-Math) and Additional Math Group Tuition Class near Admiralty MRT station.