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 $\displaystyle \frac{{{{{360}}^{o}}}}{n}$

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

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

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

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

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

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

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

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

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

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

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

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.