Consider the following statements about exterior angles of a polygon:

Statement I: Sum of exterior and interior angle on a vertex of a polygon is $360^{o}$

Statement II: Number of exterior angles is equal to number of interior angles.

Only Statement I is correct.

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Only Statement II is correct.

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Both the statements are correct.

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Both the statements are wrong.

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Solution

The correct option is B Only Statement II is correct.
Angles formed by the sides of the polygon when an adjacent side is extended are called exterior angles.

Sum of exterior and interior angle on a vertex of a polygon is $180^{o}$

Hence, Statement I is wrong.

For each interior angle, there exists a corresponding exterior angle.
$∴ Number of exterior angles = Number of interior angles$

Hence, statement II is correct.

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Similar questions

Calculate the number of sides of a regular polygon, if :

(i) its interior angle is five times its exterior angle.

(ii) the ratio between its exterior angle and interior angle is 2 : 7.

(iii) its exterior angle exceeds its interior angle by $60^{o}$ .

The rario between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :

(i) each exterior angle of the polygon ;

(ii) number of sides in the polygon.

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find :

(i) measure of each interior angle :

(ii) measure of each exterior angle and

(iii) number of sides in the polygon.

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