GATE Electrical 2021 | GA Question: 3

Question

For a regular polygon having $10$ sides, the interior angle between the sides of the polygon, in degrees, is:

• A. $396$
• B. $324$
• C. $216$
• D. $144$

Answer 1

The interior angle between the sides of the polygon $ = \frac{(n-2) \times 180^{\circ}}{n},$ where $n = $ number of sides of the polygon.

Here, $n = 10,$  therefore the interior angle between the sides of the polygon $ = \frac{(10-2) \times 180^{\circ}}{10}$

$\qquad = 8 \times 18^{\circ} = 144^{\circ}.$

So, the correct answer is $(D).$

Comments

also do watch this video https://www.youtube.com/watch?v=H8NeHSAKulM to understand the basic idea like, how the formula ((n-2) * 180°) / n is coming. The numerator part calculates the total sum of all the interior angles of the polygon, and the denominator part divides it by the total no. of sides to get the measure of one interior angle.

Answer 2

answer 144

solution- (n-2)*180=(10-2)*180=1440

where n=10 which are side decagon.

so interior angle

1440/10=144