Question

Which of the following is not true for an exterior angle of a regular polygon with $\mathrm{n}$ sides?

• A. Each exterior angle $=\frac{360°}{\mathrm{n}}$
• B. Exterior angle $=180°–$ interior angle
• C. $\mathrm{n}=\frac{360°}{\text{Exterior angle}}$
• D. Each exterior angle $=\left[\frac{\left(\mathrm{n}-2\right)\times 180°}{\mathrm{n}}\right]$

Answer 1

The correct option is D

Each exterior angle $=\left[\frac{\left(\mathrm{n}-2\right)\times 180°}{\mathrm{n}}\right]$

Explanation for correct option:

Option(D):

$\bullet$Polygon: A closed plane figure bounded by straight lines.

$\bullet$Interior angle: An angle formed inside the two adjacent sides of a polygon as shown in the figure.

$\bullet$Exterior angle: When a side of a polygon is extended, then the angle formed outside the polygon is an exterior angle as shown in the figure.

The formula to find each interior angle of a regular polygon with $\mathrm{n}$ sides $=\left[\frac{\left(\mathrm{n}-2\right)\times 180°}{\mathrm{n}}\right]$

Explanation for incorrect options

Options (A) and (C):

For a regular polygon with $\mathrm{n}$ sides

Exterior angle $=\frac{360°}{\mathrm{n}}$

$\Rightarrow$ $\mathrm{n}=\frac{360°}{\text{Exterior angle}}$

Option(B):

If interior and exterior angle are forming linear pair, then

Interior angle $+$ Exterior angle $=180°$

$\Rightarrow$ Exterior angle $=180°-$Interior angle.

Hence, the correct option is option(D)