Question

If the external angle of a regular polygon is 18°, then the number of diagonals in this polygon is:

• A. 180
• B. 150
• C. 170
• D. 140

Answer 1

Answer:

C. 170

Solution:

Given:

External angle of a regular polygon is 18°

Formula used:

The number of sides for a regular polygon with an exterior angle of x degrees is $n=\frac{360}{x}$

Number of diagonals, 

=>\frac{n\times{(n-3)}}{2}

where n is the number of sides.

Calculation: 

Substitute 18 for x in the above formula.

$n=\frac{360}{18}=20$

⇒ The number of sides for the given polygon is 20

Using the above formula for the number of diagonals, 

=>\frac{20\times{(20-3)}}{2}

=>\frac{20\times{17}}{2}

=>170

∴ The number of diagonals is 170.