# Answer the following : Find the number of sides of a regular polygon, if each of its interior angle is 3πc4. - Mathematics and Statistics

Sum

Find the number of sides of a regular polygon, if each of its interior angle is (3pi^"c")/4.

#### Solution

We know that, 1c = (180/pi)^circ

∴ (3pi^"c")/4 = ((3pi)/4 xx 180/pi)^circ = 135°

Let the number of sides of the regular polygon be n.

∴ measure of an exterior angle = (360°)/"n"

Since, the sum of the measures of an interior angle and an exterior angle of a polygon =180°,

135° + (360°)/"n" = 180°

∴ (360°)/"n" = 180° - 135° = 45°

∴ n = 360/45

= 8

Hence, the number of the sides in the polygon = 8.

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#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 1 Angle and its Measurement
Miscellaneous Exercise 1 | Q 2. II (01) | Page 12