3 Marks Question

Question 13 Marks

Find the angle measure $x$ in the given figure.

Answer

For a regular $n$-sided polygon:
Each interior angle $=180-\Big(\frac{360}{\text{n}}\Big)$ In the given figure:
$\text{n}=\text{5}$ $\text{x}^\circ=180-\frac{360}{5}$
$=180-72$ $=108^\circ$
$\therefore\text{x}=108$

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Question 23 Marks

Is it possible to have a regular polygon each of whose interior angles is 100°?

Answer

Each interior angle of a regular polygon having n sides $=180-\Big(\frac{360}{\text{n}}\Big)=\frac{180\text{n}-360}{\text{n}}$ If each interior angle of the polygon is 100°, then: $100=\frac{180\text{n}-360}{\text{n}}$ $\Rightarrow100\text{n}=180\text{n}-360$ $\Rightarrow180\text{n}-100\text{n}=360$ $\Rightarrow80\text{m}=360$ $\Rightarrow\text{n}=\frac{360}{80}=4.5$

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