Q. 13.9( 24 Votes )

Find the measure

Answer :

(i) In Regular Pentagon, all sides are of same size and measure of all interior angles are same.

The sum of interior angles of pentagon is

(n – 2) × 180° [n is number of sides of polygon)]

(5 – 2) × 180°= 540°.

Each interior angle = 540/5 = 1080

As, we know that Sum of Interior Angle and Exterior Angle is 180°

Exterior Angle + Interior Angle = 180°

Exterior Angle +108° =180°

So, Exterior Angle = 180°- 108°

=72°

(ii) In Regular Hexagon, all sides are of same size and measure of all interior angles are same.

The sum of interior angles of hexagon is

(n – 2) × 180° [n is number of sides of polygon)]

(6 – 2) × 180°= 720°

Each interior angle = 720/6 = 120°

As, we know that Sum of Interior Angle and Exterior Angle is 180°

Exterior Angle + Interior Angle = 180°

Exterior Angle +120° = 180°

So, Exterior Angle = 180°- 120°

= 60°

(iii) In Regular Heptagon, all sides are of same size and measure of all interior angles are same.

The sum of interior angles of heptagon is

(n – 2) × 180° [n is number of sides of polygon)]

(7 – 2) X 180°= 900°.

Each interior angle = 900/7 = 128.570

As, we know that Sum of Interior Angle and Exterior Angle is 180°

Exterior Angle + Interior Angle = 180°

Exterior Angle +128.57° =180°

So, Exterior Angle = 180°– 128.57°

=51.43°

(iv) In Regular Decagon, all sides are of same size and measure of all interior angles are same.

The sum of interior angles of decagon is

(n – 2) × 180° [n is number of sides of polygon)]

(10 – 2) X 180°= 1440°.

Each interior angle = 1440/10 = 1440

As, we know that Sum of Interior Angle and Exterior Angle is 180°

Exterior Angle + Interior Angle = 180°

Exterior Angle +144° =180°

So, Exterior Angle = 180°- 144°

=36°

(v) In Regular Polygon of 15 sides, all sides are of same size and measure of all interior angles are same.

The sum of interior angles of polygon of 15 sides is

(n – 2) × 180° [n is number of sides of polygon)]

(15 – 2) X 180°= 2340°.

Each interior angle = 2340/15 = 1560

As, we know that Sum of Interior Angle and Exterior Angle is 180°

Exterior Angle + Interior Angle = 180°

Exterior Angle +156° =180°

So, Exterior Angle = 180°- 156°

=24°

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