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Fill in the Blanks : in Case of Regular Polygon, with - Mathematics

Sum

Fill in the blanks:

In case of regular polygon, with

Number of sides Each exterior angle Each interior angle
(i) 6 _________ __________
(ii) 8 _________ __________
(iii)  ________ 36° __________
(iv)  _______ 20° __________
(v)  _________ _________ 135°
(vi) ________ _________ 165°
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Solution

Number of sides Each exterior angle Each interior angle
(i) 6 60° 120°
(ii) 8 45° 135°
(iii)  10 36° 144°
(iv)  18 20° 160°
(v)  8 45° 135°
(vi) 24 15° 165°

(i) Each exterior angle = `360^circ/6 = 60^circ`

Each interior angle = 180° - 60° = 120°

(ii) Each exterior angle = `(360°)/8` = 45°

Each interior angle = 180° - 45° = 135°

(iii) Since each exterior angles = 36°

∴ Number of sides = `(360°)/(36°) = 10`

Also, interior angle = 180°- 20° = 160°

(iv) Since each exterior angles = 20°

∴ Number of sides = `(360°)/(20°) = 18`

Also, interior angle = 180° - 20° = 160°

(v) Since interior angles = 135°

∴ exterior angle = 180° - 135° 

∴  Number of sides = `(360°)/(45°) = 8`

(vi) Since interior angle = 165°

∴ exterior angle = 180° - 165° = 15°

∴ Number of sides = `(360°)/(15°) = 24`

Concept: Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal
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APPEARS IN

Selina Class 6 Mathematics
Chapter 28 Polygons
Exercise 28 (B) | Q 1
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